Method and apparatus for processing high time-bandwidth signals using a material with inhomogeneously broadened absorption spectrum

ABSTRACT

Techniques for analog processing of high time-bandwidth-product (TBP) signals use a material with an inhomogeneously broadened absorption spectrum including multiple homogeneously broadened absorption lines. A first set of signals on optical carriers interact in the material during a time on the order of a phase coherence time of the homogeneously broadened absorption lines to record an analog interaction absorption spectrum. Within a time on the order of a population recovery time for a population of optical absorbers it the material, the interaction absorption spectrum in the material is read to produce a digital readout signal. The readout signal represents a temporal map of the interaction absorption spectrum, and includes frequency components that relate to a processing result of processing the first set of signals. The techniques allow processing of RADAR signals for improved range resolution to a target, as well as speed of the target, among other uses.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of Provisional Appln. 60/378,059 filed16 May 2002, the entire contents of which are hereby incorporated byreference as if fully set forth herein, under 35 U.S.C. §119(e).

STATEMENT OF GOVERNMENTAL INTEREST

This invention was made with Government support under Contract No.NAG2-1323 awarded by the National Aeronautics and Space Administration.The Government has certain rights in the invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to use of an inhomogeneously broadenedtransition (IBT) material or spatial-spectral (S²) material to achieveoptical analog signal processing, and in particular to processinganalog, large dynamic range, high bandwidth, largetime-bandwidth-product signals in the material.

2. Description of the Related Art

Real time analog large dynamic range signals with large time-bandwidthproducts (TBP, the product of a signal's bandwidth and its duration,typically considered large when in excess of 10⁴) present a challengefor conventional digital processing. Such signals can arise in a varietyof applications, including modern secure radio frequency detection andranging (RADAR), light detection and ranging systems (LIDARs), OpticalTime Domain Reflectometry (OTDR), spectral analysis and radio astronomy,among others. Other such signals are expected in a wide range oftechnical fields, including medical imaging devices, such ascomputer-assisted tomography (CAT) scans and nuclear magnetic resonanceimaging (MRI), among others.

For example, the performance of arrayed RADAR systems depends stronglyon the bandwidth and duration of signals the system can process in realtime. Current RADAR systems are limited by available signal acquisitionand processing technologies to bandwidths of a few hundred MegaHertz(MHz, 1 MHz=10⁶ Hertz, Hz; a Hz is a cycle per second). Bandwidthdirectly translates into range resolution. Some applications, such astarget recognition for missile defense systems, demand higher bandwidthsignals in the range of multiple GigaHz (GHz, 1 GHz=10⁹ Hz), at least afactor of ten greater than the available technologies. Coherent signalprocessing over multiple coherent acquisitions that are integrated meansin RADAR to obtain the Doppler shift of a return signal, as well.

Based on the foregoing, there is a clear need for developing signalacquisition and processing technologies for signals with bandwidthsgreater than 1 GHz and TBPs greater than 10⁴.

Advances in the growth and study of doped crystalline structures atextremely low temperatures (cryogenic temperatures), have revealed thatthe doping of certain rare earth ions in a certain way produces aninhomogeneously broadened transition (IBT) in these materials thatdisplay useful optical absorption properties. Materials that exhibitthis IBT are called IBT materials. The absorption demonstrates opticalfrequency selectivity over bandwidths typically far greater than 1 GHzand with frequency resolution typically far less than 100 kiloHertz(kHz, 1 kHz=10³ Hz). The ratio of bandwidth to resolution, whichcorresponds to a TBP, has been reported as high as 10⁸ in somematerials, and is generally considered useful when greater than 10⁴.Therefore processors based on IBT materials have the potential to beable to provide signal acquisition and processing technologies forsignals with bandwidths greater than 1 GHz and TBPs greater than 10⁴.

The absorption features of ions or molecules doped into inorganicmaterials are spectrally broadened by two main classes of mechanisms.Homogeneous broadening is the fundamental broadening experienced by allions or molecules independently, and arises from the quantum-mechanicalrelationship between the frequency lineshape and the dephasing time ofthe excited electron in the ion or molecule. Inhomogeneous broadeningarises from the overlap of the quasi-continuum of individual spectra ofall of the ions or molecules in the crystal, which have microscopicallydifferent environments and therefore slightly different transitionfrequencies.

The frequency selectivity can be modified locally by interaction withoptical signals that excite electrons in the molecules that serve asabsorbers from a ground state to an excited state, thereby removingthose electrons and their host ions or molecules, at least temporarily,from the population of absorbers at that location in the material.Therefore, some such materials have been used to form highly frequencyselective spatial-spectral gratings, and these materials are sometimescalled spatial-spectral coherent holographic materials (S² materials).After some time, the electrons may return to the ground state and thegrating decays. When electrons are removed from the ground state in aparticular homogeneously broadened absorption peak, a “hole” is said tobe “burned” in the absorption of the material at that frequency, aidlight at the frequency of the hole is transmitted with less absorption.Spectral gratings and spectral holes (features of spectral gratings) maybe made permanent in some applications. Spectral grating and spectralholes are general terms that are interchangeable and herein are usedinterchangeably to describe aspects of a modified absorption profile.

Some IBT materials have been used as versatile optical coherenttransient (OCT) processing devices. An OCT device is one with abroadband spectral grating in the optical range that extends overseveral homogeneous lines, and part or all of the availableinhomogeneous broadening absorption profile. All the components of anoptical spectral grating are typically formed simultaneously byrecording the spatial-spectral interference of two or more opticalpulses separated in time and/or space. When a grating is formed in theIBT material, the processor is said to be programmed, and the gratingcan be referred to as a device. This spatial-spectral grating has theability to generate a broadband optical output signal that depends on anoptical input probe waveform (referred to as a processing waveform)impinging on that grating and the programming pulses that formed thegrating.

Various optical coherent transient (OCT) devices have been disclosed,such as an optical memory (for example, T. W. Mossberg, “Time-DomainFrequency-Selective Optical Data Storage,” Opt. Lett. 7,77 1982, and“Time domain data storage,” T. W. Mossberg, U.S. Pat. No. 4,459,682,Jul. 10, 1984), a swept carrier optical memory (for example, T. W.Mossberg, “Swept Carrier Time-Domain Optical Memory,” Opt. Lett. 17,535,1992, and “Swept-carrier frequency selective optical memory and method,”T. W. Mossberg, U.S. Pat. No. 5,276,637, Jan. 4, 1994), an opticalsignal cross-correlator (for example, W. R. Babbitt and J. A. Bell,“Coherent Transient Continuous Optical Processor,” Appl. Opt. 33,1538,1994, and W. R. Babbitt and J. A. Bell, “An optical signal processor forprocessing continuous signal data,” U.S. Pat. No. 5,239,548 Aug. 24,1993), “Coherent time-domain data storage with spread-spectrum datapulse,” Yu Sheng Bai, Ravinder Kachru, U.S. Pat. No. 5,369,665, Nov. 29,1994, “Optical cross-correlation and convolution apparatus,” Thomas W.Mossberg, Yu-Sheng Bai, William R. Babbitt, and Nils W. Carlson, U.S.Pat. No. 4,670,854 Jun. 2, 1987, “Reprogrammable matched optical filterand method of using same,” Xiao An Shen, Yu Sheng Bai, Eric M. Pearson,U.S. Pat. No. 5,381,362, Jan. 10, 1995), as an optical true-time delayregenerator (see for example, K. D. Merkel and W. R. Babbitt, “OpticalCoherent Transient True-time Delay Regenerator,” Opt. Lett. 21, 1102,1996), optical spatial router (for example, W. R. Babbitt and T. W.Mossberg, “Spatial Routing of Optical Beams Through Time-domainSpatial-spectral filtering,” Opt. Lett. 20, 910, 1995, and W. R. Babbittand T. W. Mossberg, “Apparatus and methods for routing of optical beamsvia time-domain spatial-spectral filtering,” U.S. Pat. No. 5,812,318,Sep. 22, 1998), as means to continuously refresh and continuously use aspectral grating (published PCT patent application WO2000-38193“Coherent Transient Continuously Programmed Continuous Processor”) andas a means to achieve processing and variable time delay (published PCTpatent application WO2001-18818 “Method And Apparatus For Variable TimeDelay Optical Coherent Transient Signal Processing.”) the entirecontents of each of which are hereby incorporated by reference as iffully set forth herein, among others.

In these OCT devices, the readout approach typically uses high bandwidthoptical signals, such as a coherent brief optical pulse or a series ofcoherent brief optical pulses, to probe the spectral grating, whichunder certain conditions can produce optical output signals that aregenerally referred to as stimulated photon echoes. A single briefcoherent light pulse with the full spectral grating processing bandwidthstimulates a time-delayed output signal whose temporal profilerepresents the Fourier transform of the spectrum recorded in the gratingstructure. Thus a grating that represents the multiplication of thespectra of two programming pulses outputs a time-delayed signal whosetemporal profile represents the convolution of those two pulses, e.g.,the cross correlation profile of the two programming pulses. Probingwith a series of brief coherent light pulses stimulates a photon echosignal whose temporal profile represents the correlation of the probepulse with the Fourier transform of the spectrum recorded in the gratingstructure, creating real time processing ability of the probe pulse witha programmed spectral grating.

Frequency chirped pulses that are shorter in duration than the coherencedecay time of the homogeneously broadened absorption lines have beenused to probe spectral population gratings in inhomogeneously broadenedabsorbers. The result is a temporal output signal that is limited induration by the coherence decay time. For example, chirped pulses can beused to store and recall temporal data (Y. S. Bai, W. R. Babbitt, and T.W. Mossberg, “Coherent Transient Optical Pulse Shape Storage/RecallUsing Frequency-Swept Excitation Pulses,” Opt. Lett. 11, 724 (1986).)and used to generate arbitrary waveforms (Z. Barber, M. Tian, R. Reibel,and W. R. Babbitt, “Optical pulse shaping using optical coherenttransients”, Opt. Exp. 10, 1145-1150 (2002)). The chirp rates of thechirped probe pulses used in these examples are fast and do not generatea temporal map of the structure of the spectral population grating.These chirped probes generate a temporal output signal that represents acollective readout of the spectral population grating, not itsindividual components, with bandwidths of the temporal output typicallyequal to the bandwidth that was excited in the medium, i.e. thebandwidth of the chirp. High bandwidth detectors are thus needed torecord the outputs from this manner of chirped readout.

While potentially useful in many applications, the approach of readoutcreating an optical pulse or series of optical pulses at the fullbandwidth of processing suffers, at present, from the limitedperformance in dynamic range of photo-detectors and digitizers that areneeded to make a measurement of any high bandwidth optical signal.Existing high bandwidth detectors and analog to digital converters(ADC's also called “digitizers” herein) have limited performance (andare also far more expensive) as compared to lower bandwidth detectorsand digitizers. For example, currently available detectors withbandwidths greater than 1 GHz have about 30 deciBels (dB) of dynamicrange. Dynamic ranges of about 90 dB or more are preferred, which axepresently available for photo-detectors with bandwidths on the order of1 MHz and ADCs with operation sample rates on the order of 10Mega-samples per second (Ms/s).

In addition to the detection difficulties with high bandwidth signals,inefficiencies of such approaches of readout require that the highbandwidth probes have high power. Such high power probes are difficultor expensive to create, further impeding the implementation of thesereadout approaches.

Based on the foregoing, there is a clear need for a processor of highbandwidth signals that makes use of the TBP potential of IBT materialsand that does not suffer the disadvantages of prior art approaches.

SUMMARY OF THE INVENTION

Techniques are provided for optical analog processing of hightime-bandwidth-product (TBP) signals. Multiple processing acquisitionscan be integrated in the IBT material. The low bandwidth, high qualityanalog optical output signal from the device represents the results ofhigh bandwidth optical processing and includes, in some embodiments,integration over several sets of interacting signals. The analog outputsignal is photo-detected and digitized with high precision to produce adigital output. In one embodiment, a method includes causing an inputsignal on an optical carrier to interact in a material with aninhomogeneously broadened absorption spectrum including a plurality ofhomogeneously broadened absorption lines to record an interactionabsorption spectrum. Within about a population recovery time for apopulation of optical absorbers in the material, the interactionabsorption spectrum is read to produce a readout signal that representsa temporal map of the interaction absorption spectrum. The readoutsignal indicates frequency components of the input signal

According to an aspect of the invention, wherein an aspect is a set ofembodiments, a method includes causing a first set of signals on opticalcarriers to interact in an IBT material. The IBT material has aninhomogeneously broadened absorption spectrum including a plurality ofhomogeneously broadened absorption lines. A population of opticalabsorbers in the material that are in an excited state return to theground state on a scale characterized by a population recovery time. Thefirst set of signals on optical carriers interact in the material duringa time on the order of a phase coherence time of the homogeneouslybroadened absorption lines to record an analog interaction absorptionspectrum. Within a time on the order of the population recovery time,the interaction absorption spectrum in the material is read to produce areadout signal. The readout signal represents a temporal map of theinteraction absorption spectrum, and includes frequency components thatrelate to a processing result of processing the first set of signals.

According to some embodiments of this aspect, the interaction absorptionspectrum in the material is read by measuring absorption of a frequencychirped optical signal directed into the material. In some embodiments,the measurement bandwidth of the interaction absorption spectrum coversall or part of the actual absorption spectrum bandwidth.

In some embodiments, the measurement of the interaction absorptionspectrum produces a readout signal with a bandwidth that issubstantially less than a minimum bandwidth of the first set of signals.

According to some embodiments of this aspect, before a readout time onthe order of the population recovery time expires after the first set ofsignals, an additional set of signals on optical carriers is directedalong the same spatial mode in the material as the original set ofsignals. The additional set is directed along the mode at a repetitiontime after an immediately previous set of signals. The interactionabsorption spectrum integrates a spectrum that represents an interactionamong signals in the additional set of signals.

According to some embodiments of this aspect, the first set of signalson optical carriers interact differently in each spatial mode of a setof spatial modes through the material to record a corresponding set ofinteraction absorption spectra. Reading the interaction absorptionspectrum includes reading the corresponding set of interactionabsorption spectra to produce a corresponding set of readout signals.Each readout signal includes frequency components that relate to aprocessing result of processing the signals in a corresponding spatialmode.

In some of these embodiments, a particular signal from the first shot ofsignals is frequency shifted by a different frequency shift for eachspatial mode of the corresponding set of spatial modes. The methodfurther includes determining a Doppler shift based on a particularfrequency shift applied at a particular spatial mode associated with aparticular readout signal.

According to another aspect of the invention, an apparatus includes asignal input port for receiving a signal set of one or more shots ofinput signals. The apparatus includes a material with an inhomogeneouslybroadened absorption spectrum including a plurality of homogeneouslybroadened absorption lines. The apparatus also includes a first opticalcoupler to direct a plurality of modulated optical signals onto thematerial in a set of one or more spatial modes. The modulated opticalsignals are based on each shot of input signals in the signal set. Themodulated optical signals are directed onto the material within about aphase coherence time of a homogeneously broadened absorption line torecord an interaction absorption spectrum that represents spectralprocessing of the shot. The apparatus further includes a source of aprobing signal and a detector. The detector measures, with, time, areadout signal based on the interaction absorption spectrum and theprobing signal. The readout signal represents a temporal map of theinteraction absorption spectrum and includes frequency components thatrelate to a processing result of processing the first plurality ofsignals.

According to another aspect of the invention, a system includes anoptical analog processing device, a RADAR signal conditioner, and aRADAR processor. The optical analog processing device includes a signalinput port, a IBT material, an optical coupler, a source of a probingsignal, and a detector. The signal input port receives a signal set ofone or more shots of input signals. The IBT material has aninhomogeneously broadened absorption spectrum including a large numberof homogeneously broadened absorption lines. The optical coupler directsmodulated optical signals based on each shot onto the material in a setof one or more spatial modes within about a phase coherence time. Thephase coherence time is related to a homogeneously broadened absorptionline. The optical coupler directs the modulated optical signals onto thematerial to record an interaction absorption spectrum that representsspectral processing of the shot. The detector measures, with time, areadout signal based on the interaction absorption spectrum and theprobing signal. The readout signal represents a temporal map of theinteraction absorption spectrum and includes frequency components thatrelate to a processing result of processing the first plurality ofsignals. The RADAR signal conditioner selects a first set of one or moresignals and a second set of one or more signals. The first set of one ormore signals is based on one or more RADAR transmitted signals. Thesecond set of one or more signals is based on one or more receivedsignals, which are based on the one or more RADAR transmitted signalsafter reflection from a target. The conditioner sends the first set ofsignals and the second set of signals to the signal input port of theanalog optical processing device. The RADAR processor determines rangeor Doppler shifts, or both, with high resolution to the target based onthe readout signal in the analog optical processing device.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements and in which:

FIG. 1A is a graph that illustrates a homogeneously broadened absorptionspectral line and an inhomogeneously broadened absorption spectrum in anIBT material;

FIG. 1B is a graph that illustrates time scales associated with signalsprocessed in the IBT material, according to an embodiment;

FIG. 1C is a time line that illustrates timing of several examplesignals processed in the IBT material, according to an embodiment;

FIG. 1D is a graph that illustrates an example interaction absorptionspectrum formed in an IBT material, according to an embodiment;

FIG. 1E is a graph that illustrates a cross-correlation curve as aprocessing result, according to an embodiment;

FIG. 2 is a flow diagram that illustrates at a high level a method forprocessing high TBP signals using an IBT material, according to anembodiment.

FIG. 3A is a block diagram that illustrates an optical analog processor,according to an embodiment;

FIG. 3B is a block diagram that illustrates a component of frequencyshifter array, according to an embodiment;

FIG. 4 is a block diagram that illustrates a RADAR processing systemthat uses an optical analog processor, according to an embodiment:

FIG. 5A is a block diagram that illustrates an experimental setup fordemonstrating delay processing, according to an embodiment near 1536 nm;

FIG. 5B is a block diagram that illustrates an experimental setup fordemonstrating delay processing, according to an embodiment near 793 nm;

FIG. 6A is a graph that illustrates portions of readout signals from anIBT material, after interaction by a pair of pulses at each of multipledelays, according to an embodiment near 1536 nm;

FIG. 6B is a graph that illustrates peaks in cross correlation curvesgenerated from the readout signals of FIG. 6A, according to anembodiment near 1536 nm;

FIG. 6C is a graph that illustrates a comparison between crosscorrelation curves generated from readout signals for pulses with fixeddelay after integration over different numbers of shots of such pulses,according to an embodiment near 1536 nm;

FIG. 6D is a graph that illustrates a dependence on the number of shotsfor signal strength in different portions of a cross correlation curvefor two pulses with fixed delay, for a particular pulse power, accordingto an embodiment near 1536 nm;

FIG. 6E is a graph that illustrates a dependence on the number of shotsfor signal strength in different portions of a cross correlation curvefor two pulses with fixed delay, for a different pulse power, accordingto an embodiment near 1536 nm;

FIG. 7A is a graph that illustrates a dependence on the delay time of apeak in a cross correlation derived from a readout signal from an IBTmaterial, according to an embodiment near 793 nm;

FIG. 7B is a graph that illustrates a dependence on power and number ofshots of the peak in a cross correlation derived from a readout signal,according to an embodiment near 793 nm;

FIG. 7C is a graph that illustrates a dependence on number of shots ofthe peak in a cross correlation derived from a readout signal usingmultiple pulse patterns and a fixed pulse pattern, according to anembodiment near 793 nm;

FIG. 7D is a graph that illustrates a dependence on multiple pulsepatterns of the cross correlation derived from a readout signal,according to an embodiment near 793 nm; and

FIG. 8 is a block diagram that illustrates a digital computer systemupon which portions of an embodiment of the invention may beimplemented.

DETAILED DESCRIPTION

A method and apparatus and system for processing high TBP signals aredescribed. In the following description, for the purposes ofexplanation, numerous specific details are set forth in order to providea thorough understanding of the present invention. It will be apparent,however, to one skilled in the art that the present invention may bepracticed without these specific details. In other instances, well-knownstructures and devices are shown in block diagram form in order to avoidunnecessarily obscuring the present invention.

Embodiments of the invention are described in the context of processingRADAR transmitted and received signals for improved range resolution andimproved resolution of Doppler shifts, but the invention is not limitedto this context. Embodiments of the invention may be practiced forprocessing of fewer signals, more signals and different signals,including processing any signals that use different frequency bandsand/or spatial configurations to represent data, including LIDAR data,OTDR data, noise LIDAR data, laser RADAR data, radio frequency (RF)signal data (such as noise RADAR data. RF spectral analysis data and REspectral estimation data), radio astronomy data and data in othertechnical fields, such as medical imaging data.

For example, embodiments of the invention maybe used in active RADAR forsingle-element antenna, or large multi-element phased arrays, for rangein mid- to high-pulse Doppler, target identification, moving targetindications, and for synthetic and inverse synthetic aperture RADAREmbodiments may be used in passive RF receiver systems for interceptingtransmissions, for detecting stealth communications, and for analyzingfrequency-hopping radio. Embodiments may be used in radio astronomy foranalyzing radio astronomy signals, and for searching forextra-terrestrial intelligence. Embodiments may be used in LIDAR andlaser RADAR for wind shear measurements, atmospheric monitoring andweather prediction, for pollution monitoring, and for space-basedtracking of satellites and other targets.

1. IBT Materials

FIG. 1A is a graph that illustrates a homogeneously broadened absorptionspectral line 110 and an inhomogeneously broadened absorption spectrum120 in an IBT material. The frequency axis 102 represents frequencies(f), in Hz, increasing to the right. The absorption axis 104 representsthe population (N(F)) of absorbers, which are available to absorb light,and is related to the absorption of light per unit length along aspatial path into the material. The graph depicts a homogeneouslybroadened absorption spectral line 110 centered on line center frequency103, which has a homogeneous line bandwidth proportional to thereciprocal of a time T2.

As explained in more detail below, a large number of homogeneouslybroadened absorption lines for absorbers spread throughout aninhomogeneous crystal results in an inhomogeneously broadened absorptionspectrum 120. The inhomogeneously broadened absorption spectrum 120 hasa band center frequency 105 and an inhomogeneous spectrum bandwidth 122,also represented by the symbol B, or B_(M) for the material bandwidth,or δω_(I). The band center frequency is in the optical band, whichencompasses frequencies from 100 to 1000 TeraHz (THz, 1 THz=10¹² Hz).However, the inhomogeneous spectrum bandwidth 122, B, is typically lessthan a few THz—large compared to the bandwidths available for RADARprocessing but small compared to the hundreds of THz bandwidth of theoptical band.

The intrinsic frequency selective properties of IBT materials arederived from the sharp resonance δω_(H) of electrons in ions andmolecules in cryogenic solids, where the resonance δω_(H) isproportional to the homogeneous line bandwidth, e.g. homogeneous linebandwidth 112 in FIG. 1A. These sharp resonances can be below 1 kHz, andare typically in the range of 1 kHz to 100 kHz. Inversely proportionalto the homogeneous line bandwidth is the phase coherence time, T2, alsocalled the homogeneous dephasing time, which is the time scale forcoherent, phase-sensitive transitions between the ground state and theexcited state for a homogeneous set of absorbing electrons.

When an electron makes the transition to the excited state because oflight impinging at a particular location in the material, there is onefewer absorber at that location. Therefore, the population of absorbersdecreases and the absorption decreases at that location. If there arefew enough absorbers in the location, or if enough photons excite enoughelectrons, the decrease in the population of absorbers, and theresulting decrease in absorption at the particular line frequencies thatmatch the photon frequencies is appreciable. For example, after enoughphotons with frequencies within absorption line 110 impinge on alocation in the material, the absorption peak associated with absorptionline 110 at that location decreases, and the absorption spectrum 120 hasa dip centered near the line center frequency 103.

Members of a population of excited electrons gradually return to theground state, and the population of absorbers, along with theabsorption, returns to its initial value. The time scale associated withthis process is the population recovery time, TG. For example, the dipin absorption spectrum 120 at line frequency 103, described above, fillsin exponentially with a time constant on the order of TG. The value ofTG depends on the material and the return path through any intermediatestates to the ground state.

The ability of IBT materials to process broadband signals stems from theinhomogeneous broadening bandwidth, δω_(I), e.g. inhomogeneous linebandwidth 122 in FIG. 1A. The inhomogeneous broadening is typicallycaused by defects found in the crystalline host of the absorbingmolecule or ion. These local defects, the “inhomogeneities,” causesimilar ions to have different resonant frequencies, but do not broadenthe individual homogeneous resonances. The broad inhomogeneous bandwidth122 determines the processing bandwidth of the material.

An appropriate IBT can be found in at least three types of materialsystems:

-   1) a system with a two-level transition between a ground electron    state |1> and an upper electron state |2>;-   2) part of a three-level system of electron states with an    intermediate bottleneck state |3> that slows down the decay process    back to the ground state |1>; and-   3) part of a multiple-level system, with three or more levels,    including state |3> and zero or more other states |n> where n>3,    which may or may not provide gain. In all of these systems, T1 is    the population decay time of the upper state |2>, T2 is the    coherence time of the transition between lower state |1> and upper    state |2>, and TB is a decay time of a bottleneck or pumped state    |3>. In all of these systems, the radiation field of the interacting    light beams only couples states |1> and |2>. In the multiple-level    system with gain, there is typically one or more electron states    above or below states |1> and |2>. A population of electrons in the    resonant states |1> and |2> is provided by adding energy to    (pumping) electrons at natural state |3> with electromagnetic waves    at entirely different frequencies from the interacting optical    beams. The excited electrons can go to state |1> directly or    indirectly by decaying from state |2> or some other state |n>.    2. IBT Material Time Scales

FIG. 1B is a graph that illustrates time scales associated with signalsprocessed in the IBT material, according to an embodiment. The time axis152 represents time increasing to the right. The percentage axis 154represents the percentage of absorbers relative to an initial number ofabsorbers in a given state at time zero, increasing upward.

It is assumed for purposes of illustration that a material is selectedin which the population recovery time, TG, is long compared to the phasecoherence time T2. Curve 163 represents the percentage of absorbers in ahomogeneous crystal environment that are coherent after excitation. Thispercentage decreases exponentially on a time scale 164 equal to thephase coherence time T2, which is inversely proportional to δω_(H).Curve 165 represents the percentage of absorbers in the excited state,relative to an initial population in the excited state after passage ofan optical signal. This percentage decreases exponentially also, butmore gradually, with a longer time scale 166 equal to TG.

Also shown in FIG. 1B is the useful bit duration 162 for codedmodulation (phase and/or amplitude), which is the inverse of the usefulbandwidth δω_(I). Bit durations shorter than bit duration 162 generatefrequency components that do not fall within the useful bandwidth δω_(I)(the inhomogeneous spectrum bandwidth 122). Since δω_(I) is greater thanδω_(H), the bit duration is necessarily less than the phase coherencetime T2.

For optical signals to interact coherently in the material, theinteracting signal or signals must reach the same location in thematerial within a time on the order of the phase coherence time T2.Thus, to correlate a reference signal and its delayed reflectedcounterpart, as in the RADAR problem, the reflected signal must impingeon the same volumetric location in the material within a useful timeinterval relative to T2 after the reference signal arrives at thatlocation. Thus, a material should be selected with a phase coherencetime large enough to encompass the delays of interest

3. Signal Time Scales

FIG. 1C is a time line that illustrates timing of several examplesignals processed in an IBT material, according to an embodiment. Forpurposes of illustration, the signals are discussed in the context ofdetermining the delay between a signal and its replica, which is asimple surrogate for determining the range to a target from atransmitted and reflected RADAR pulse.

The optical signals are inherently analog in nature and can be anyrepresentation of information by modulation techniques or anycombination of modulation techniques (amplitude, frequency, phase,etc.). Thus, any method of representing a value on an optical carriermay be used. For purposes of illustration, it is assumed that the valueis a bit that represents one of two opposite phases for the opticalcarrier. Such encoding of values on an optical carrier is called binaryphase-shift keying (BPSK). In other embodiments, other forms of encodingmay be used. For example, the phase may be allowed to varyproportionally to a value being encoded. In this case the value is notbinary and the bit value axis would be replaced with a variable valueaxis. The value on the variable axis may be called a chip value and theunit of information a chip instead of a bit.

The time axis 172 represents time increasing to the right. The bit valueaxes 174 a, 174 b (collectively referenced hereinafter as bit value axes174) represents one of two values for each bit; one value represented bythe top of each axis 174, and another by the bottom of each axis 174. Itis assumed for purposes of illustration that the bit duration, eachbit's width on the time axis, is the minimum useful bit durationinversely proportional to the useful bandwidth 122. The optical carrierhas a frequency within the inhomogeneously broadened absorption spectrum120 of FIG. 1A or 1D. It is assumed for purposes of illustration thatthe optical carrier frequency is at or near the band center frequency105.

In the embodiment depicted in FIG. 1C, a first signal 182, representing,for example, a transmitted RADAR pulse, is made up of a sequence ofbits, represented by the vertical oscillation between bit values. Theellipses imply that the signals can be longer than those shown, so thatthe signals can be temporally overlapping in time. A second signal 184,representing, for example, a reflected RADAR pulse, includes a similarsequence of bits that arrive after a delay time 175 a. In practice forthe RADAR case, this second signal will be attenuated and altered byexternal factors, and therefore a noisy analog waveform. In general, thereceived signal can be a superposition of multiple target returns. Forpurposes of illustration, only one perfect target return is shown. Forthese two signals to effectively interact in the IBT material, the delaytime 175 a should be on the order of the phase coherence time or less.The first signal and the second signal constitute a first set of signals180, called a shot. In other embodiments, mole signals may be includedin the first set of signals to interact.

FIG. 1C also depicts a second set of signals 185 that includes a thirdsignal 186 and a fourth signal 188 that represents the delayedcounterpart of the third signal 186 with a delay 176 b. For the RADARcase with a pulse repetition interval, the third signal arrives afterthe first signal by a repetition interval 177, represented by the symbolτ_(R). In the general case, the first and second signal can becontinuous, thus with no repetition interval. In this case the signalsinteract constantly over the phase coherence time T2 as a sliding timewindow of interaction. In illustrated embodiments, described in moredetail below, the repetition interval τ_(R) is typically greater thanthe phase coherence time T2, so that the third and fourth signalsminimally interact with the first and second signals.

4. Spectral Results

If the signals have sufficient intensity, then the absorption spectrumin the material where the two signals interact reflects a complexspectral interaction of the spectral content of the two signals, asdescribed in more detail below. FIG. 1D is a graph that illustrates anexample interaction absorption spectrum 190 formed in an IBT material,according to an embodiment. The axes 102, 104, the band center frequency105 and the inhomogeneously broadened spectrum 120 are the same as theyare in FIG. 1A. The example interaction absorption spectrum 190 differsfrom the inhomogeneously broadened absorption spectrum 120 by an amountthat represents the spectral content of the interaction of the signalsin the first set.

The mathematical operations of analog signal processing (e.g.,convolutions and correlations in time) can be implemented as frequencydomain multiplications. As is well known, the interaction of two signalsin the same volume through an IBT material yields the multiplication ofcross terms in the complex Fourier transforms of the temporal inputsignals modified by the effects of a finite phase coherence time. Thefollowing theoretical explanation is provided to help describeembodiments of the invention; however the invention is not limited tothis theory.

It is assumed that the first signal 182 is represented by the temporalfunction E1(t) of time t; and that the second signal 184 is representedby the temporal function E2(t−τ_(D)), where the two signals areseparated by delay τ_(D). The Fourier transforms of the two signals arerepresented by F1(ω) and F2(ω)e^(−iωτ) ^(D) , respectively. The terme^(−iωτ) ^(D) represents a complex phase angle. Both signals interact ata location in the IBT material within the delay time τ_(D). Theinteraction complex power spectrum, represented by |F12(ω)|², is thesquare of the sum of the of the electric fields, which follows inEquation 1.|F 12(ω)|² =|F 1(ω)+F 2(ω)e ^(−iωτ) ^(D) |² =|F 1(ω)|² +|F 2(ω)|² +F1*(ω)F 2(ω)e ^(−iωτ) ^(D) +F 1(ω)F 2*(ω)e ^(+iωτ) ^(D)   (1)The interaction power spectrum includes the power spectra of the firstand second signals as the first two terms in the last line of Equation1, and cross terms that contain the interference of the power spectrumof each pulse. The cross terms include the full amplitude and phaseinformation of each pulse and a strong periodic component with frequencyinversely proportional to the delay τ_(D) between the signals.

The magnitude of the Fourier transform of the interference terms yieldsa cross correlation curve with a peak at the periodic component thatrepresents the delay τ_(D). FIG. 1E is a graph 191 that illustrates across-correlation curve 196 as a processing result, according to anembodiment with a strong periodic component. The time axis 192represents delay time between the two signals, increasing to the right.The amplitude axis 194 represents the amplitude of cross correlation ofthe two signals at a given delay, increasing upward.

The curve 196 is derived by taking the Fourier transform of theinteraction absorption spectrum. The peak 197 indicates that the signalscorrelate most strongly when the second signal contains components ofthe first signal that are shifted by the delay 198. For the first signal182 and the second signal 184, the delay 198 associated with peak 197 isexpected to equal the delay 175 between those two signals.

With the appropriate intensities of the interacting signals and theappropriate number of available absorbers, the interaction spectrum ofthe signals can be represented in the material as an interactionabsorption spectrum, also referred to as a spectral population grating,with a large dynamic range.

The interacting beams carrying the signals may be collinear, passingthrough the same spatial modes, or intersect at one or more angles,along two or more intersecting spatial modes. In embodiments in whichthe same spatial mode is used for the interacting signals, the gratingproduced is purely spectral and the processing stage is simplified. Thereadout stage can be along the same spatial mode or slightly angled tothe processing modes. In embodiments in which different interactingbeams are introduced on two or more spatial modes that are angled, thegrating produced is both spectral and a spatial. This grating can beread along a specially chosen readout direction, either coherently orincoherently. Although for the general case, a grating is both spectraland spatial, the processed information due to the interaction of signalsis purely spectral at any given specific location. Unless otherwisestated, these spatial-spectral population gratings are referred to asspectral population gratings or interaction absorption spectrahenceforth.

5. Integration

Subsequent signals that arrive after T2 but within TG create aninterference spectrum that is recorded as a spectral population gratingin addition to the spectral population grating previously recorded inthe material. This sum of the interaction spectra of multiple shotsenhances features of the spectral population grating that are common toeach shot. Thus introducing another set of interacting signals tomeasure the same thing, e.g., the delay between transmittal andreception of a RADAR signal can add to the dynamic range of the spectrumrecorded in the material. This process is referred to as integration.

However, the recorded spectrum decays away over die population recoverytime TG. Therefore, integration should be completed before a time on theorder of TG, and the recorded spectrum can be measured within severalTG, as desired, with respect to signal strength considerations.

FIG. 1C shows the relationship between coherent interaction andincoherent integration of spectral content in signals that areintroduced at repetition interval 177. The first set of signals 180,called a shot, are introduced to the IBT material typically within atime on the order of T2 to form an interaction spectrum that is recordedin the material. A second shot of signals 185 is introduced afterrepetition interval 177, represented by the symbol τ_(R), that should belong compared to T2 to insure that coherences from the first shot havesufficiently decayed so as not to significantly interfere withcoherences from the second shot, as desired with respect to signalstrength considerations. However, this is not a requirement and dependson the implementation. The signals in the second shot interact to formanother coherent interaction resulting in an interaction spectrum thatis recorded in addition to the spectrum already there, as long asrepetition interval τ_(R) is short compared to the population recoverytime TG. For example, to include N shots before the population recoversby a factor ˜⅓, N×τ_(R) should be less than TG.

If the property of interest is the delay time, it is not necessary thatthe first signal 182 in the first shot 180 and the third signal 186 inthe second shot 185 be identical. The periodic component representingthe delay will be integrated even if the power spectra of the individualsignals are not the same. Therefore, in the RADAR delay problem,different transmit signals may be used in each shot. Furthermore, in themost general case, the signals in each shot are not identical. When thesignals are different in each shot, the integration of the interactionspectra still provides the cross-correlation of signals. In this generalscenario, there is no lower bound on τ_(R). For example, in radioastronomy, where continuous signals comprise a single set, the crosscorrelation of these signals is desired, and it is a rare occurrencewhen signals are identical.

6. Array Processing

The spectral processing described above occurs in a part of the materialilluminated by both the processing signals, which may be only onespatial mode through the material for determining correlations, or anintersection volume of two or more spatial modes. Separate processingcan be performed in other volumes using other spatial modes through thematerial. The separate processing may include processing signals fromdifferent systems and burning holes for data storage or for stabilizinglaser frequencies. The separate processing can be parallel operationsfor parallel signals. For example, in array antennas with multipleelements, the signals from all the elements could be processed inparallel. The use of multiple different spatial modes in the materialsimultaneously is called array processing.

For example, in the RADAR application, the return signal from a movingtarget is not only delayed in time, but also shifted in frequency by anamount called the Doppler shift that is proportional to the targets'longitudinal velocity. When a reference signal based on the transmittedsignal interacts with a frequency shifted return, the individualcorrelation is processed with the frequency difference corresponding toa mismatch of the spectral content and corresponding phase shift.However, when integrating multiple spectrum correlations, the strengthof integrated spectral correlations are diminished when a referencesignal based on the transmitted signal interacts with a frequencyshifted return. In RADAR systems, Doppler shifts are typically in therange of 100 Hz to 100 kHz.

The frequency shift of the return can be determined by replicating thetransmitted signal multiple times in various spatial modes, and shiftingeach replica by a different frequency shift (including zero and negativefrequency shifts in some embodiments). The reflected signal isreplicated the same number of times but with no frequency shift. Eachreplica of the reflected signal interacts with a different frequencyshifted replica of the transmitted signal in a different spatial mode.Different interaction spectra are recorded in the different spatialmodes. The integrated interaction absorption spectrum that leads to thestrongest frequency components in the readout signal, or eventually thegreatest correlation peak, is the one with the transmitted replicashifted by an amount closest to the Doppler shift in the reflectedsignal. Thus a strong correlation peak and the Doppler shift aresimultaneously determined using array processing in the multiple spatialmodes available in the IBT material.

7. Readout, Detection and Analog-to-Digital Conversion for PostProcessing

Reading the absorption spectrum recorded in the IBT material can beachieved by an optical signal whose carrier frequency is a puresinusoidal signal that is swept slowly compared to the period of thecarrier over the used frequencies in the absorption spectrum 120,without any other appreciable optical tones present.

Slow readout of the content of the spectral grating can be achieved bymapping the spectral structure in time using the chirped optical pulsedescribed above. This process reduces the measurement bandwidth to theorder of the spectral feature size of interest in the spectral grating.Since the desired high bandwidth processing is done in the material andrecorded there, the sweep rate can be selected to be slow enough so thatthe features of the absorption spectrum are mapped onto the transmittedfrequency chirped optical pulse. The transmitted pulse can be detectedusing low bandwidth photo-detectors to generate a low bandwidth readoutsignal. This electronic readout signal can be digitized with lowbandwidth ADCs. This provides a major advantage over conventional highbandwidth readout using photon echo based effects, because low bandwidthoptical to electrical (O/E) photo-detectors and ADCs are maturetechnologies with high dynamic ranges and also low cost.

In some embodiments, reading the frequency dependent absorption is clonewith a sweep rate typically on the order of 1/(τ_(Dmax))², whereτ_(Dmax) is the maximum, resolvable delay, to ensure sufficient temporalresolution. A consequence of this is that the bandwidth of detection isreduced to on the order of 1/τ_(Dmax) rather than B, the bandwidth ofthe inhomogeneously broadened absorption spectrum. For example, ifτ_(Dmax)=1.0 μs, then the sweep rate can be 1.0 MHz/μs and the detectionbandwidth is 1 MHz.

In some embodiments, the grating can be read with a slow coherentoptical frequency swept pulse but by utilizing photon echo effects. Insuch cases, the output signal consists of stimulated photon echo signalsfrom the grating due to the frequency swept pulse, which are by naturedelayed from the coherent optical frequency swept pulse and can be on aunique spatial mode due to the input beam geometry. This geometry cangenerally be considered a box geometry, with the signals n=1, 2, 3 (n=1,first processing waveform; n=2, second processing waveform; n=3, chirpedreadout pulse) forming three vertices of a box with 2 and 3 on oppositecorners. This is such that for a given vector, K₀, the individual unitwavevectors are k_(n)=K₀+δK_(n), where every |δK_(n)| is equal, δK_(n)is perpendicular to K₀ and δK₃=−δK₂. The phase matching condition isk _(S) =k ₃ +k ₂ −k ₁,with the output signal direction forming the fourth spatial mode vertexof the box. The output signal and a replica of the readout chirp with afixed time reference can be made to coherently interfere with each otheron the detector to produce a low bandwidth electronic readout signalthat can be digitized with an ADC. The choice of the chirp rate andgrating feature size will determine the bandwidth of detection anddigitization that is necessary.

The low bandwidth readout signal, once detected and digitized, can bepost processed to determine its frequency content. This frequencycontent (f) corresponds to the time delay (τ_(D)) information containedin the spectral population grating, converted via division of thefrequency by the chirp rate (γ) used for readout, i.e., τ_(D)=f/γ. As iswell known, the chirp rate y is the readout bandwidth (Br) divided bythe time of readout (Tr). The digital post processing step to determinethis frequency content can utilize any discrete Fourier Transform orFast Fourier Transform algorithms or methods that are known as the stateof the art. By consequence, the maximum detection frequency bandwidth(Bd) is equal to the maximum time delay (τ_(Dmax)) multiplied by thechirp rate, i.e., Bd =γ*τ_(Dmax).

FIG. 2 is a flow diagram that illustrates at a high level a method forprocessing high TBP, large dynamic range signals using an IBT material,according to an embodiment. Although the steps are shown in a particularorder for the purpose of explanation, in other embodiments, the stepsmay be performed in a different order or overlap in time or a step maybe omitted. For example, the step 202 of receiving the shots can overlapin time the step 210 of writing the initial shot into the material; andthe step 270 of the readout stage may occur continuously andsimultaneously with the step 250 of the integration stage.

In step 202, a set of one or more shots, each of two or more signals toprocess, are received. The shots received in step 202 include all shotsthat are to be integrated in the processing. The first shot may beprocessed in the following steps while later shots are being received instep 202. In other embodiments, each shot includes only one signal.

Step 210 represents an initial writing stage. After a time on the orderof one or more population recovery times from any previous processingsteps, the signals in the first shot are directed to a set of one ormore spatial modes in an LBT material within a time that, in someembodiments, is on the order of the phase coherence time T2. If arrayprocessing is performed with the signals of these shots, some or all ofthe signals, modified or not, are directed to different spatial modes ofthe IBT material during step 210. For example, different phase shiftedreplicas of a transmitted RADAR signal are directed to different partsof the material, each with a replica of the received RADAR signal.

Step 250 represents an integration stage. In the illustrated embodiment,in step 250, at a time τ_(R) that is on the order of the phase coherencetime T2 after the immediately previous shot of signals was directed tothe material, signals from a subsequent shot are directed to thematerial along the same spatial modes as used in step 210. All signalsin the shot are directed to the same spatial modes. Step 250 is repeatedfor all shots to be integrated after the initial shot.

Step 270 represents a readout stage. Step 270 may be performed at anytime during or after step 210 and repeated as often as desired. Readoutsperformed past the population recovery time TG after the first shot iswritten in the material do not include the effects of the first shot, soin the preferred embodiment, the readout of the first set of shots isperformed before a time on the order of the population recovery timeafter the first shot is directed to the IBT material. The integratedresult is obtained from step 270 after the last shot is directed ontothe material and before the population recovery time after the initialshot. The resultant readout signal of step 270 is a temporal map of theintegrated interaction absorption spectrum recorded in the material. Ifarray processing is used, an array of readout signals is produced.

In the preferred embodiment, the readout is performed with a frequencychirped optical signal that sweeps the used frequencies of theinhomogeneously broadened absorption spectrum slowly enough to measureabsorption features of interest to create a low bandwidth optical signalthat can be well measured with low bandwidth high quality detectors andADCs. If the frequency chirped optical signal is of low enoughintensity, then it does no appreciably change to the spectrum (i.e., isnon-destructive).

Step 280 represents a post processing stage. In step 280, the readoutsignal is processed to determine a processing result. For example, thedigital Fourier transforms of the digital readout signals are computedto generate digital correlation on curves associated with each ofmultiple frequency shifts in different spatial modes. In someembodiments, the multiple correlation curves are output to generate atwo dimensional range-Doppler ambiguity function. For a single target,in some embodiments, the correlation curve with the largest peak isdetermined, and the peak of that curve is used to derive a delay orrange, and the frequency shift associated with that curve is used toderive a Doppler shift. In some embodiments, many such peaks aredetected. In some embodiments, the post processor interpolates to aDoppler shift based on the peak amplitudes and associated frequencyshifts of several correlation curves.

Using the method 200, high bandwidth, analog, large TBP signals withlarge dynamic range can be processed in the IBT material, and theresults can be readout with high quality low bandwidth detectors anddigitizers.

9. Optical Analog Device

FIG. 3A is a block diagram that illustrates an optical analog device300, according to an embodiment. The optical analog device 300 includesan optical source module 310, a signal input module 320, a readoutsource module 330, an optical amplifier module 340, an array processormodule 350, a S² material module 360, and an output module 370. In otherembodiments, more or fewer modules may be included.

The modules are connected by optical couplers 302 represented in FIG. 3Aby thick solid lines. Input ports 328 to the signal input module 320 andoutput ports 378 from the output module 370 are electrical couplers 304,such as wire and coaxial cable, represented by thin solid lines. Inother embodiments, input ports or output ports, or both may include oneor more optical couplers or wireless radio couplers or both. Variouscomponents in the modules are also shown connected by electricalcouplers 304 in the illustrated embodiment.

9.1 Optical Source

The optical source is selected to have a frequency f0=ω0/2π in the bandof the inhomogeneously broadened absorption spectrum 120 and to bestabilized so that frequency fluctuations are smaller than thehomogeneously broadened absorption line bandwidth (˜1/T2) during thelifetime of the spectrum (TG). As such, a frequency-stable laser acts asthe optical master oscillator for the device. The laser/masteroscillator stability is an important device parameter, as the frequencycharacteristics of the master optical oscillator affect the overallcoherent processing performance. As stated above, this line bandwidthshould be as narrow and stable as possible over the desired integrationtime, and certain stability is demanded to generate processing resultsthat are coherent and can thus be integrated over the integration time.The value (˜1/(100*τ_(Dmax)) is a general guideline for large dynamicrange processing; for example, to resolve delays of 1 μs, stability of10 kHz would be required. In the illustrated embodiment, the opticalsource module 310 includes a laser 312 controlled by an electricalconnection to a frequency stabilizer component 314.

To perform the integration of a spectral population grating, therequirement exists that the phase difference between the opticalcarriers carrying the interacting pulses be relatively constant over theintegration time. For example, if the carrier frequency changes toω0+δω0 between two carriers for two interacting signals, then a changein the phase difference (δφ) between two interacting pulses, 1 and 2,results—with a value of δφ21=δω0*τ_(D), where τ_(D) is the delay betweenthe two interacting pulses and φ represents phase. This phase differenceshould be relatively constant over the integration time. That isδφ21_(k)−δφ21_(j)<<π  (3a)between any shots k and j of interacting pulses within time TG. Thisimplies that the short term frequency stability of the source should bebetter thanδω0<<π/τ_(D)  (3b)over any time period within TG. When the same optical source (or a groupof multiple, locked sources) is used to generate both interactingoptical beams, then the long-term frequency drift of the centerfrequency is inconsequential, provided all optical signals of intereststay well within δωI.

In some embodiments, the laser 312, or the frequency stabilizercomponent 314, or both, are controlled by an electronic processor thatis either internal to or remote from the device 300, or both. Anelectronic processor is described in more detail in Section 12.

In some embodiments, the laser 312 is an external cavity diode laser(ECDL) master oscillator based on the Littman-Metcalf cavityconfiguration well known in the art. These devices are commerciallyavailable (e.g., from New Focus Inc. of San Jose, Calif., USA). Thesecommercial lasers have appropriate specifications on poster (˜100milliW, mW, 1 mW=10⁻³ W), tunability (˜100 GHz mode-hop-free) andspatial mode. The frequency stability of the commercial lasers isspecified to ˜300 kHz on a 10 milliseconds (ms, 1 ms=10⁻³ s) time frame.However, the required level of frequency stability is not currentlyavailable from commercial units. An extra frequency stabilizingcomponent 314 is included in the illustrated embodiment.

In some embodiments, the frequency stabilization component 314 uses theEBT material as a reference, based on techniques described, for example,in U.S. Pat. No. 6,516,014, the entire contents of which are herebyincorporated by reference as if fully set forth herein. The frequencylocking techniques utilize transient, regenerated spectral holes in theIBT material burned by the continuous wave (cw) optical oscillator.Active stabilization is achieved using a Pound-Drever-Hall technique,where an error signal is derived in stabilizer 314 from the deviation ofthe carrier instantaneous frequency to the spectral hole burned earlierby the carrier. This error signal is negatively fed back to a diodecurrent control input on laser 312 in real time to achieve activefrequency stabilization. This approach is inherently compatible withoptical device 300 using the IBT (S²) material module described in moredetail below. A different spatial mode in the IBT material may be usedto burn the spectral hole. No additional cryogenic equipment is neededto support this technique to stabilize laser 312. Using this technique,the best performance of ECDL stabilization has been specified to 20 Hzroot-Allen deviation over 10 ms in an IBT material composed of Tm:YAG(0.1 at. %) at 1.9K—a dramatic 2 parts in 10¹³ of frequency stability(N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone,Physics Review B Vol 62, 2000, p. 1473). A laser frequency stability of1 kHz over 10 ms is achievable based on locking to Tm:YAG (0.1 at. %) at4K.

In one embodiment, the frequency stabilizer component 314 includesseveral commercial off-the-shelf components, such as electro-opticmodulators (EOM), photo-detectors, and radio frequency (RF) oscillatorsand mixers

In the illustrated embodiment, the frequency-stabilized laser 312generates an optical carrier at frequency f0 that is used in subsequentmodules. Therefore laser 312 directs the optical carrier onto an opticalcoupler 302 for delivery to the signal input module 320.

9.2 Signal Input

Signal input module 320 includes multiple input ports 328, such as inputports 328 a, 328 b, 328 c. Each input port 328 is electrically connectedto an electro-optic modulator (EOM), such as EOM 322 a, 322 b, 322 c,respectively, collectively referenced hereinafter as EOM 322. Althoughthree input ports with corresponding EOM are shown in FIG. 3A, in otherembodiments, more or fewer input ports and EOM may be used.

Each EOM is connected to the optical source 310 through an opticalcoupler that brings the optical carrier beam with frequency f0. Theoutput of each EOM is a modulated optical beam, or modulated opticalsignal, which is directed through an optical coupler to the IBTmaterial, through any intervening modules. The modulated optical signalfrom each EOM 322 is based on the optical carrier and the signal inputon the input port 328 connected to the EOM 322. In some embodiments,electro-optic phase modulators (EOPMs) are used to modulate the opticalcarrier in phase in proportion to the sign and magnitude of the appliedRF voltage.

In some embodiments, the EOM 322, or other components, or both, arecontrolled by an electronic processor that is either internal to orremote from the device 300, or both.

Electro-optic conversion of RF signals onto the optical carrier in someembodiments is achieved using high bandwidth waveguide EOMs. Thesecomponents are commercially available for operation at wavelengths from780 nanometers (nm, 1 nm=10⁻⁹ meters) to 1600 nm. These wavelengthscorrespond to optical frequencies from 385 THz to 188 THz. Use of thesehigh quality devices (and the associated electronics to drive them) hasbecome widespread due to their deployment in telecommunications systems.For example, appropriate EOMs are commercially available from EO-SpaceInc. of Redmond, Wash., USA. An embodiment of device 300 tailored forRADAR processing utilizes two of these devices per antenna element.

In the RADAR example, both the RADAR reference signal (a replica of thetransmitted waveform) and return signals (an attenuated version of thetransmitted waveform, buried in noise and Doppler shifted) are modulatedonto an optical carrier, each on an independent EOM.

The performance of the signal input module is determined by thefrequency response, linearity and additive noise of the componentsutilized to build the module. In some embodiments, a RF amplifier isincluded between the input ports and the corresponding EOM. AppropriateRF amplifiers are commercially available from many vendors (e.g.,Agilent, Palo Alto, Calif., USA and Picosecond Pulse Labs of Boulder,Colo. USA).

9.3 Readout Source

The readout source 330 provides a slow frequency chirped pulse to readthe interaction absorption spectrum recorded along each spatial mode inthe IBT material. In the illustrated embodiment, the readout source 330includes a laser 332 and an optical modulator such as EOM 334electrically controlled by an RF frequency sweep generator 336. Theoptical carrier signal output by the laser 332 is input through anoptical coupler into the modulator, e.g. EOM 334 where it is modifiedaccording to the electrical signals from frequency sweep generator 336.The output is the slow frequency chirp on the optical coupler directedto the next module, the optical amplifier module 340. In otherembodiments, other sources for a slow frequency chirp are used. Directdigital synthesis of RF frequency sweeps at 1 Gs/s are commerciallyavailable from Analog Devices of Norwood, Mass., USA, for example modelnumber AD9858. Any method known in the art at the time the opticaldevice is made may be used. In some embodiments the laser 332 isreplaced by an optical coupler to the optical source 310 laser 312.

In some embodiments, the laser 332, or the modulator, (e.g., EOM 334) orthe sweep generator 336, or some combination, are controlled by anelectronic processor that is either internal to or remote from thedevice 300, or both.

In the illustrated embodiment, the readout module creates a singlesideband, suppressed carrier (SSB-SC) tone or carrier frequency thatsweeps (or chirps) over the readout bandwidth Br of interest within thefrequency band B_(M) of the inhomogeneously broadened absorptionspectrum 120. For example, an acousto-optic modulator (inherentlySSB-SC) is being used in the demonstration described below in Section11. In other embodiments, other sidebands may be present that do notappreciably interfere with obtaining the readout signal in the band Brthat may be only a portion of the material bandwidth B_(M).

In a preferred embodiment, the critical performance specifications ofSSB-SC modules are linearity of chirp, phase noise, amplitude noise,carrier suppression and sideband cancellation, such that these do notlimit the device dynamic range.

In some embodiments, the laser 332 is a second slave oscillator,frequency agile and offset from the master oscillator. This slave ECDLis referenced and locked to the master ECDL, and may have the capabilityto discretely tuned to readout various portions of the spectralpopulation grating.

9.4 Optical Amplifier

The optical amplifier module 340 includes one or more opticalamplifiers, such as optical amplifier 342. The broadband modulatedoptical signals from the signal input module 320 are amplified toachieve intensities needed to record appreciable spectra in the IBTmaterial. The modulated optical signals from the readout source module330 are amplified to detect transmission through the IBT material. Thetwo optical couplers entering and exiting the optical amplifier 342carry the slow frequency chirped pulse from the readout source module330 and the modulated optical signals from the signal input module 320,respectively.

In some embodiments, the optical amplifiers in module 340 are controlledby an electronic processor that is either internal to or remote from thedevice 300, or both.

Any optical amplifier known in the art with appropriate characteristicsat the time the optical processor is built may be used. Several opticalamplifier approaches exist and depend on the optical wavelength ofoperation. At 1550 nm, 194 THz, Erbium doped fiber amplifier (EDFA)components are a mature and widespread technology, and other approachessuch as semiconductor optical amplifiers and Raman fiber amplifiers arealso reaching maturity. At present time, near 800 nm, 375 THz, amplifiertechnology is evolving with applications and market demand. Severalapproaches are possible, including tapered waveguide semiconductoroptical amplifiers (SOAs), injection locking to high powered diodelasers, and fiber amplifiers. In addition, both thulium doped fiberamplifiers and Raman fiber amplifiers are evolving technology for 793nm.

9.5 Array Processor

The array processor module 350 includes an array coupler 352 to combinemodulated optical signals associated with one shot into multiple spatialmodes through the IBT material for array processing. The array coupler352 shows multiple optical couplers emerging for each optical couplerentering from optical amplifier 342. Any method known in the art may beused to direct optical signals into the desired spatial modes, includingreplicating one or more signals. The array coupler also replicates theslow frequency chirped pulse and directs any replicas, at least asneeded, onto multiple spatial modes. The number of spatial modes and themodifications to the optical signals, if any, performed in the arrayprocessor module 350 depends on the processing to be performed. It iswell within ordinary skill in the art to dispose lenses, mirrors, beamsplitters, phase shifters, and other devices to direct one or more inputoptical signals on one or more optical couplers into one or more outputoptical couplers or focus those beams on an image plane of the IBTmaterial.

In the illustrated embodiment, Doppler shift detection is to beperformed, so the array coupler sends signals to a frequency shifterarray 354 to frequency shift some signals before directing them ontospatial modes through the IBT material.

The array processor module 350 combines the aspects of spatialmultiplexing to create a bank of parallel processing operations. In someembodiments more or fewer components are included in the array processor350, or the array processor module is omitted altogether, and only onespatial mode is used in the device 300 for recording and readingabsorption spectra.

In some embodiments, the array coupler, or the frequency shifter array,or both, are controlled by an electronic processor that is eitherinternal to or remote from the device 300, or both.

The frequency shifter array 354 can be achieved by any method known inthe art. In one embodiment, a tilting mirror is illuminated normally andimaged accordingly. In other embodiments, the mirror may be illuminatedat a different angle. At the axis of tilting in the center of themirror, no Doppler is produced, while on one side the mirror movestowards the beam and Doppler upshifts are produced that get larger asthe distance away from the tilting axis increases. Similarly on theother side, the mirror appears to be moving away with a correspondingDoppler downshift that linearly increases as the distance away from theaxis increases. This embodiment may suffer from mechanical instabilitiesand precision issues that acousto-optic approaches with no moving partswould not have.

A more reliable, straightforward approach is to create an array of beamsand to use an array of acousto-optic frequency shifters (AOFS), one oneach beam. Each of the AOFS devices would modulate the input light at acenter frequency with a corresponding offset frequency shift, forexample, one device at frequency f₁, the next at f₁+δ, the next atf₁+2δ, and so on. This approach has no technical holdups, but suffersfrom needing a AOFS and RF driver for each spatial mode.

Other embodiments use two acousto-optic modulators instead of an arrayof frequency shifters to achieve similar results. In an illustratedembodiment, two commercially available acousto-optic devices (AODs) aredisposed in a counter propagating RF wave propagation geometry, and eachdriven by the same slow RF chirp. Counter propagating AOD geometrieshave been employed previously for optical processing application(“Acousto-optic time integrating frequency scanning correlator” N. J.Berg, I. J. Abramovitz, M. W. Casseday, J. N. Lee, U.S. Pat. No.4,421,388). FIG. 3B is a block diagram that illustrates an embodiment350 a of frequency array processor 350. Component 350 a includes twoAODs 381 a, 381 b each fed by a corresponding chirp generator 382 a, 382b, respectively. In some embodiments, generators 382 a, 382 b are thesame. With one AOD reverse imaged onto the other, and operated inconjugate orders, this assembly can be used to produce a spatial arrayof frequency-shifted optical reference beams. This can be programmed toproduce the required array of frequency shifts 389 by driving input ofthe AOD with an appropriate RF chirp. The resulting frequency shiftsvary linearly over a device aperture up to a maximum which can cover anominal frequency range of 10 kHz in 10 ms by choosing the chirp rate as1 MHz/μs. The RF frequency chirp for the Doppler module can be createdin generators 382 a, 382 b with a chip that performs direct digitalsynthesis of low bandwidth analog waveforms (DDS chip) and controller,in some embodiments.

In another embodiment, one acousto-optic device is used. The device isdriven in a first direction by a slow RF chirp. In this embodiment, anarray of beams output by the device are directed back through the samedevice driven by the same slow RF chirp, but in a direction that isopposite to the first direction relative to the direction of propagationof the beams.

The operation of these embodiments can be interpreted as a pair ofcontroller propagating moving lenses whose quadratic phase factorcancels out leaving a linear time varying prismatic phase factor just asin the case of the linearly tilting mirror. Alternatively, it can beinterpreted as an implementation of the well-known symmetric chirpalgorithm, producing an array of Doppler shifted beams to be used forparallel array Doppler processing.

By modulating the reference beam first with the signal of interest,amplifying and creating a spatial array, and then feeding this array ofsignals to an spatial array frequency shifting device, each spatial modehas the information of the reference and a corresponding desiredfrequency shift.

9.6 Material Module

The material module 360 includes an IBT material 364 (also called an S²material) maintained at cryogenic temperatures in a cryostat 362 withoptical windows for passing optical signals into the material.

Scientific Materials Corporation (SMC) of Bozeman, Mont. is currentlythe sole supplier of high purity rare-earth-doped spatial-spectralcrystalline materials used in the illustrated embodiments. Materialscurrently exist with desirable homogeneously broadened line widths andinhomogeneously broadened absorption bandwidths. Two candidate materialshave properties suitable to demonstrate processing of RADAR signals. Thefirst material is yttrium aluminum garnet (Y₃Al₅O₁₂) doped with thulium(represented by the symbol Tm:YAG); the second material is yttriumsilicate (Y₂SiO₅) doped with erbium (represented by the symbol Er:YSO).

TABLE 1 Properties of two typical IBT materials. Property \ Material >Tm:YAG Er:YSO Wavelength 793.375 nm 1536.140 nm Center frequency377.86500 THz 195.15800 THz Rare-Earth dopant thulium erbiumConcentration varies (e.g., 0.1 at. %) varies (e.g., 0.001 at. %)Bandwidth ~20 GHz ~0.5 GHz (variable to 20 GHz in other hosts) Linewidth(1/T2) varies (<200 kHz) varies (<200 kHz) Ratio (~TBP) varies (>1000)varies (>1000) Population decay time ~10 ms ~10 ms (TG)

The IBT materials typically require cooling to cryogenic temperaturesfor operation. The illustrated embodiment calls for cooling to the 4K to5K level. Optical absorption contributes to local heating in thematerials that needs to be cooled. Present day, reliable, turnkey,maintenance-free for 20,000 hours and low vibration, closed cyclecryo-coolers are commercially available for 1.0 W of cooling power at 4K(Cryomech Corp. of Syracuse, N.Y. USA). These systems are findingwidespread deployment in magnetic resonance imaging systems and areimproving in cost and efficiency. Current specifications of vibrationlevels are 10 μm (microns, 1 micron=10⁻⁶ m) on the 1.4 Hz scale, whichis within the displacement tolerance for spatial modes over the 10 msintegration time scale. Industrial efforts to dampen the smallvibrations to 1 μm displacement continue.

In some embodiments, the cryostat (cryo-cooler) is control led by anelectronic processor that is either internal to or remote from thedevice 300, or both.

The signal to noise ratio (SNR) of spectra recorded in the IBT material,or the dynamic range, or both, ultimately depends on the absorbing ionsper spectral channel, given the absorbers available in a volumeassociated with each spatial mode. A parameter Γ representing thematerial absorbers per unit bandwidth per unit volume (e.g., ions/(Hzm³)) is derived from a doping density and host. For example, for Tm:YAG(0.1 at %) with a 20 GHz bandwidth, Γ=7×10¹⁴ ions/(Hz m³). A collinearspatial mode, used by interacting beams, which has a diameter of 50 μmthrough a crystal 5 mm (millimeter, 1 mm=10⁻³ m) long, has aninteraction volume of 10⁻¹¹ m³. In such a volume of Tm:YAG (0.1 at %)there are 7000 ions per Hz; and, therefore, there are on the order of10⁹ ions in the spatial mode per spectral channel (one homogeneousbroadened line) of about 150 kHz linewidth. Thus there is a potentiallygreat dynamic range for absorption spectral amplitudes in thesematerials.

9.7 Output Module

The output module 370 includes an O/E photo-detector array 372 connectedby electrical coupler to an ADC 374, which is connected by electricalcoupler to post processor 376. In some embodiments, the post processormay be omitted. In some embodiments that use a single spatial mode, asingle detector is used in place of detector array 372.

In some embodiments, the detector array 372, or the converter 374, orpost processor 376, or some combination, are controlled by an electronicprocessor that is either internal to or remote from the device 300, orboth.

The readout technique of device 300 achieves a low bandwidthrepresentation of the result of high bandwidth signal processing.Consequently, tremendous advantages in the comparative noise equivalentpower (NEP) and dynamic range for a low bandwidth (˜1 MHz) detector overhigher bandwidth (1-10 GHz) photo-detectors can be exploited.

In some embodiments, a detector in the photo-detector array 372 utilizescertain well-known photo-detection circuits that cancel the effects oflaser intensity noise by several orders of magnitude, making very smallsignal variations on a large background easy to detect, yieldingperformance that is close to being limited by shot noise. This approachis well suited for the readout techniques and increasing the backenddynamic range. The second purpose in the utilization of such intensitynoise canceling detectors is that proper design of the bandwidth of thedetector will remove the effects of the intensity variation of thechirped laser from the grating readout.

Following detection, the signal undergoes an analog-to-digitalconversion prior to post processing. Here again the device 300 has theadvantage of not requiring high bandwidth ADCs for post processing ofhigh bandwidth wave forms. For example, at the time of this writing, a16-bit ADC at 20 Megasamples per second, AD9260, is available fromAnalog Devices of Norwood, Mass. for under $50. For high bandwidthsampling, an 8-bit ADC at 20 Gs/s (in Tektronix scope TDS7000, fromTektronix, Inc of Beaverton, Oreg., United States.) is available for aprice that is about three orders of magnitude greater than the AD9260.

10. RADAR Processing System

FIG. 4 is a block diagram that illustrates a RADAR processing system 400that uses an optical analog device 480, according to an embodiment. Aconventional RADAR system includes a radio frequency transmitter 430electrically connected to a RADAR transmit antenna 438, and a RADARreceive antenna 452 electrically connected to a radio frequency receiver450. In some embodiments, the transmit and receive antennae are thesame. A RADAR transmitted signal 442 is transmitted from the RADARtransmit antenna and impinges on a target 440, which may be moving. Oneor more surfaces on the target 440 reflect the transmitted signal as areflected RADAR signal 444 that is received by the RADAR receive antenna452. The transmit and received waveforms are sent to a digitalprocessor, such as digital processor 494 to determine the range to andspeed of target 440.

A conventional RADAR system commonly generates the signal transmitted byradio frequency transmitter 430 in a baseband code generator 410 and anintermediate frequency converter 420. The baseband code generatorgenerates the bits or chips that make up the code to be transmitted. Thesignal may be as simple as a voltage that changes at the bit rate,usually much less than 10 GHz. In sophisticated systems the basebandcode generator generates a different code for each transmitted pulse tohinder the ability of the target to detect the transmitted RADAR signal442, enhance the security of the RADAR system, and reduce sidelobecontributions. The baseband code can be used to modulate radio frequencytransmissions directly, which are often in frequencies at or above 1GHz, using a RF mixer or mixers. However, in many systems the code ismixed with an intermediate frequency (IF) electronic signal in an IFconverter 420, and the IF signal is used to modulate the RF carrier, forexample with binary phase shift keying (BPSK).

Similarly, a conventional RADAR system commonly decodes the reflectedsignal (including delays, Doppler frequency shifts and noise) receivedby radio frequency receiver 450 in an intermediate frequency converter460 and a baseband code converter 470. The IF converter 460 steps theradio carrier frequency down from the GHz range to the lowerfrequencies. The baseband converter 570 generator generates the bits orchips that make up the received signal. The baseband received signal maybe as simple as a voltage that changes at the bit rate.

According to the illustrated embodiment, signals from the RADAR systemare input to an optical analog device 480 at signal input ports 482 a,482 b (collectively referenced hereinafter as signal input ports 482).The optical analog device 480 is an embodiment of the optical analogdevice 300 depicted in FIG. 3, configured for RADAR signal processing,either by internal controllers or external controllers such as digitalprocessor 494 or by internal hardwired components. The optical analogdevice 480 processes the signals input at input ports 482, and generatesan output signal at output port 488. The output signal is used directlyin some embodiments. In the illustrated embodiment, the output signal isused as input to a digital processor 494, such as a computer, whichdisplays or further processes the output signal.

In some embodiments, some signals from the RADAR system are first inputto an electric signal integral delay device 492 before being passed tothe optical analog device 380. The electric signal integral delay device492 is described in more detail below. If the electric signal integraldelay device 492 is omitted, the signals depicted as input to the delaydevice 492 are instead input directly to the input port 482 a of opticalanalog device 480.

The optical analog device can process multiple shots of signals. Eachshot includes a pair of signals: a reference signal that represents thesignal transmitted by the RADAR system; and a return signal thatrepresents the reflected RADAR signal received by the RADAR system. Theprocessing by the optical analog device 480 can be performed either in aconfiguration where the reference signal and return signal are atbaseband bit rates, or at an IF carrier modulated versions of thebaseband signal, or at the RADAR frequency transmitted and reflectedpulses, for example, depending oil the performance of theelectro-optical modulators 322. If the baseband bit rates are used asthe input signals, then a baseband reference signal is communicated toinput port 482 a of the optical analog device 480 through electricalcoupler 412 (and electrical signal integral delay 492, if present); anda baseband return signal is communicated to input port 482 b of theoptical analog device 480 through electrical coupler 472. If the IFfrequency signals are used as the input signals, then an IF referencesignal is communicated to input port 482 a of the optical analog device480 through electrical coupler 422 (and electrical signal integral delay492, if present); and an IF return signal is communicated to input port482 b of the optical analog device 480 through electrical coupler 462.If the radio frequency signals are used as the input signals, then aradio reference signal is communicated to input port 482 a of theoptical analog device 480 through electrical coupler 432 (and electricalsignal integral delay 492, if present); and a radio return signal iscommunicated to input port 482 b of the optical analog device 480through electrical coupler 452.

In the illustrated embodiment, the optical analog device 480 providesprecision delay measurements with delay resolutions that correspond tofine range resolution, e.g., a range resolution of centimeters, up to amaximum delay that corresponds to a maximum range, e.g., a few hundredmeters. To determine precision delay measurements at longer ranges, thereference signal can be delayed a known amount, until the remainingdelay is within the maximum delay detected by optical analog device 480.This is accomplished in electrical signal integral delay device 492. Forexample, the reference signal can be routed through a length of cablethat is known to be a certain length longer than the length of cablefrom the return signal (the integral delay) or routed a certain numberof times through a loop of known length (an integral delay) to producean integral number of fixed delays (the integral delay).

In some embodiments, the output of the optical analog processing device480 is a digital signal that represents the absorption measurements. Insome embodiments, a processor within the optical analog device 480(e.g., post processor 376 in FIG. 3) preconditions the readout signal asneeded and extracts the relevant content of the mapped interactionabsorption spectrum. In some embodiments, a processor within the opticalanalog device 480 performs analysis on the set of readout signalscorresponding to the set of frequency-shifted reference pulses todetermine the delay-Doppler profile. In some embodiments, the internalprocessor also takes the Fourier transform of the spectra. In someembodiments, the internal processor also generates the cross correlationcurves, and determines the best peak, the associated Doppler shift anddelay, and the corresponding range, or some combination of theseresults.

In any embodiment, the digital processor 494, if present, does anyprocessing needed to convert from the output of the optical analogdevice 480 to the desired processing result. In various embodiments, theprocessing result is used in any way deemed beneficial for the RADARprocessing system, including the generation of new baseband codes.

11 Use of RADAR Processing System

In RADAR range and Doppler processing applications, a complex RF pulsesequence is transmitted. The delayed received signal is analog innature, attenuated, with extra noise, frequency shifted by an amountrelated to the velocity of the target, and with reflections combinedfrom possibly multiple surfaces. Correlation between the transmitted andreturn signals yields the round-trip time for the RADAR pulse as a delayτ_(D). When the reference and return signals are modulated on the sameoptical carrier in optical analog device 480, the IBT records theirspectral interference with a modulation period 1/τ_(D). Thus τ_(D) isderived from the spectra recorded in the IBT material.

The RADAR system should process pulses of duration Tp and bandwidth Bp.The optical analog device 480 limits Bp to be less than or on the orderof the bandwidth B_(M) (also represented by the symbol δω_(I)) of theinhomogeneously broadened absorption spectrum in the IBT material.Similarly, the device 480 limits the coherently processed pulse durationTp to be on the order of the phase coherence time. T2; and limits anintegration time Ti to be on the order of the population recovery time,TG.

The pulses are repeated at a pulse repetition frequency (PRF) with acorresponding pulse repetition interval τ_(R)=1/PRF. Integration of Ncoherent spectral interactions theoretically increases the intensity ofthe main frequency component (1/τ_(D)) by N², while the noise grows moreslowly, with the first power of N. The integration also providesresolution for frequency analysis of return signals to determine anyDoppler shifts. The main frequency component (1/τ_(D)) is the same nomatter which coded waveform is used as the transmitted signal; thereforeagile codes can be used, changing the codes from shot to shot. The codescan be selected to have zero mean, and a large number of such zero meancodes has at least two advantages. First, they increase the security ofthe RADAR system. Second, they increase the processing gain throughdistributed spread spectrum techniques, thus increasing the overallratio of integrated; peak root mean square (rms) value to the rms ofsidelobes.

In practice, the intensity of the main frequency component grows atslightly less than N² and is modeled as N^(2α), where α is a coefficientsuch that 0<α≦1, until a compression point is reached where the materialbegins to saturate and run out of ground state absorbers to record theinteraction. In addition to the main component at (1/τ_(D)), there areother cross terms, or “spurs,” that record harmonics of each singledelay and “intermods” from two or more delays in each shot. When thesespurs grow larger than the noise floor, they limit the dynamic range ofthe recorded spectrum. The overall device performance will be anoptimization of signal strength and dynamic range.

For Doppler processing, frequency-shifted reference signals are directedto parallel spatial modes as narrow-band Doppler filters. Doppler shiftsof interest are typically in the range of 100 Hz to 100 kHz. Such shiftscan be produced by the AODs described above. In this technique, the RFreference signal is modulated onto the optical carrier beam and thensubsequently diffracted by counter propagating AODs that createspatially separated frequency offset versions of the reference that areimaged onto the IBT material, as described above. Over multiple shots,the cumulative phase difference for unmatched frequency shiftedreferences causes the grating to wash out at the corresponding spatialmodes. At the same time, the closely matched frequency shiftedreferences that match the Doppler shift in the return pulse accumulate astrong grating in its corresponding spatial mode. All spatial modes canbe read out to produce a complete range-frequency shift data set inwhich the proper frequency shift demonstrates the greatest amplitude inthe main frequency component (1/τ_(D)).

The properties of the readout stage depend on the maximum resolvabletime delay (τ_(Dmax)) and the chirp rate γ, as described above. Thecorresponding range bin of the processor is R_(bin=c*τ) _(Dmax)/2, wherec is the speed of light. The fundamental limit on τ_(Dmax) is related toT2, the phase coherence time. Several readout properties can be definedas follows:

Readout bandwidth (Br) Br ≦ Bp Readout rate (γ) γ = Br/Tr Detectionbandwidth (Bd) Bd = γ * τ_(Dmax)Table 2 lists possible delays (τ_(Dmax)) and their associated detectorbandwidth (Bd) for varying values of γ.

TABLE 2 Example delays and associated detector bandwidth (Bd) in MHz.τ_(Dmax) γ = 1 γ = 2 γ = 2.5 γ = 4 γ = 5 γ = 10 (μs) MHz/μs MHz/μsMHz/μs MHz/μs MHz/μs MHz/μs 1 1 2 2.5 4 5 10 2 2 4 5 8 10 20 2.5 2.5 56.25 10 12.5 25 4 4 8 10 16 20 40 5 5 10 12.5 20 25 50 10 10 20 25 40 50100Because delays longer than the longest delay bin can be handled bysynchronizing the delay bin with front end electronics, e.g., in theelectrical signal integral delay device 492 in FIG. 4, initialembodiments use short delay bins with small latency TL, high resolution,and large dynamic range.

An example RADAR system has a value for pulse repetition frequency (PRF)of 50 kHz and a value for pulse length Tp of 10 μs, and a pulsebandwidth Bp of about 1 GHz. A suitable IBT material would have a valuefor T2 of 10 μs and a bandwidth B of 1 to 10 GHz to process pulses witha TBP from 10,000 to 100,000 at each resolvable spatial mode through thematerial. PRF is limited by the time between shots.

The upper limit on the number of integrated shots Nmax is theintegration time times the fastest PRF allowed by the IBT material. Forexample, for Ti of 10 ms and the maximum allowed PRF of 50 kHz, themaximum value for N is 500 shots.

In any RADAR, the delay resolution depends on the bandwidth and signalto noise ratio (SNR) of the received signal but is typically limited bythe delay resolution of the processor itself. The delay resolution ofthe optical analog device 480 can be selected based on the readoutbandwidth of the integrated interaction absorption spectrum recorded inthe IBT material and the dynamic range based on the absorbers.

The Doppler resolution is ultimately related to the inverse of theintegration time and the SNR. Thus, a Doppler resolution of about 100 Hzis achievable for Ti of 10 ms if the SNR is sufficiently high. A 100 HzDoppler resolution corresponds to a velocity resolution that depends onthe RADAR carrier frequency (e.g., for 15 GHz RF carrier frequency,velocity resolution is 1 meter per second for 100 Hz Dopplerresolution). To exploit this resolution over a large range of Dopplershifts, to cover a large velocity range, a large number of frequencyshifted reference signals are introduced on different spatial modesthrough the IBT material. The number of spatial modes is limited by thesize of the crystal and the volume of resolvable spatial modes withsufficient dynamic range to record an interaction absorption spectrum.Finer Doppler resolution can be achieved by digital post processing.

12. Demonstration

Signal delay processing results have been generated for twodemonstration embodiments, one embodiment at optical frequencies near195 THz (1536 nm) (Z. Cole, T. Bottger, R. Krishna Mohan, R. Reibel, W.R. Babbitt, R. L. Cone and K. D. Merkel, Applied Physics Letters, 81,3525), and the other embodiment at optical carrier frequencies near 378THz (793 nm)(“Demonstration of the Spatial-Spectral Coherent HolographicIntegrating Processor (S2-CHIP) for Analog rf Signal-ProcessingApplications,” K. D. Merkel, Z. Cole, R. K. Mohan, W. R. Babbitt,GOMACTech-03 Conference Proceedings, Paper 26.8, Tampa, Fla., Apr. 3,2003).

12.1 Demonstration Near 1536 nm

FIG. 5A is a block diagram that illustrates an experimental setup 500for demonstrating delay processing near 1536 nm, according to oneembodiment. An external cavity diode laser (ECDL) 512 a is centered at1536 mm and frequency stabilized to a transient spectral hole in onespatial location of a 5 mm long Er³⁺:Y2SiO5 (0.001 at. %) material 560 aat 4.2 K in a 3.0 Tesla (T) magnetic field. This IBT material has aB_(M) of 0.5 GHz. As part of the frequency stabilizing mechanism in thisembodiment, a beam from the ECDL 512 a is amplified at Erbium-dopedfiber amplifier (EDFA) 542 and coupled through fiber couple CC) 502 balong optical path 503 a. The beam is modulated in electro-opticmodulator 511 to form a locking signal that burns a spectral hole in aspatial mode through the IBT material 560 a and is detected withdetector 514. The signal detected by detector 514 is used by lockcircuitry 515 a to control the ECDL 512 a by electronic coupler 504.

A beam from the stabilized laser is fiber coupled at FC 502 a and splitinto two beams, one along optical path 503 c for modulating withinteracting pulses (“processing”), and the other along optical path 503b for readout and frequency locking.

The processing beam along path 503 c is modulated by a 1 GHzelectro-optic phase modulator (EOM) 522 a driven by a pulse patterngenerator (PPG) 526 a and RF amplifier 524. After modulation, theprocessing beam is amplified by EDFA 544 a and fiber coupled in FC 502d. A chopper (not shown) creates a 4 ms off-window in the processingbeam to allow readout about 0.5 ms into this window. The processing beamis directed onto non-polarizing beam splitter cube 540 a for directingonto the IBT material 560 a.

The readout (“probing”) beam along optical path 503 b is amplified inEDFA 542 and fiber coupled in FC 502 c, then operated upon by anacousto-optic modulator (AOM) 530 a to create a linear frequency-sweptpulse. A mirror, 532 a and the non-polarizing beam splitter cube 540 adirect the readout beam, collinearly with the processing beams, onto aspatial mode focused on an approximately 50 μm spot on the IBT material.A gating AOM 570 deflects the temporally attenuated readout beam towardsa 125 MHz photo-detector 572 a. The output from the photo-detector isdisplayed on oscilloscope 574 a and digitized. The digital signal isprocessed by computer 576.

For the experimental demonstration of coherent integration of dynamiccodes, each processing shot (e.g., first set 180 in FIG. 1C) consists ofan M-bit binary phase-shift keyed (BPSK) waveform (e.g., first signal182, representing a RADAR reference signal and a single time delayedreplica (e.g., second signal 184 representing a RADAR return signal),where a unique shot, comprising a unique pulse pair, identified by j=1,2, . . . N was introduced every τ_(R) (e.g., repetition interval 177).

The delay τ_(D) (e.g., delay 175 a) is fixed for all shots. Eachprocessing shot contains a unique, zero-mean BPSK waveform and its timedelayed replica. Theory and E simulation shows that using dynamic codesin coherent integration enhances the primary component (oscillating withperiod 1/τ_(D)) while the other spectral features (e.g., temporalsidelobes) change each shot, so that a ratio of the temporal peak tomaximum sidelobe rms approaches M². While not necessary for achievingcoherent integration, dynamic coding was used in the illustratedexperimental demonstration.

The optical carrier beam was continuously BPSK modulated, such that eachsignal was modulated at 0.5 Gbps (Gbps=10⁹ bits per second) and betweenshots the optical carrier was square wave ( . . . 101010 . . . )modulated at 1 Gbps (not depicted), resulting in frequency sidebandsoutside the material's 0.5 GHz absorption profile.

For all experiments, M is 200 (thus each coded waveform was 200 bits,i.e., 400 ns) and the repetition interval τ_(R) is 5 μs. The probe pulsepower is 10 μW and swept over ˜15 MHz of the grating at a rate of 0.2083MHz/μs using a 165 MHz carrier and the AOM 530. Post processing of thesignal digitized from the transmitted probe beam consists of filteringto minimize the strong low-frequency components of the unabsorbedenvelope and calculating the magnitude squared of the Fourier transformof the result, using a fast Fourier transform (FFT) process.

FIG. 6A is a graph 610 that illustrates portions of readout signals froman IBT material, after interaction by a pair of pulses at each ofmultiple delays, according to an embodiment. The time axis 612 indicatesthe time during the frequency sweep of the readout beam, and is relatedto frequency in the absorption spectrums time values are indicated inμs. The amplitude axis 614 indicates the relative magnitude oftransmission, increasing upward, and is inversely proportional toabsorption. Amplitude is given in arbitrary units. Each curve 616 athrough 616 p represents the readout signal after 800 shots at 25 mWpower with a fixed value for the delay. Each curve is displacedvertically a different amount to allow features to be viewed. The fixedvalue of the delay increases from 0.5 μs for curve 616 a through 2.0 μsfor curve 616 p, at 0.1 μs per curve 616. The curves 616 represent thefiltered raw data, showing grating structure after subtraction ofunabsorbed background. A dominant oscillation in the absorption, withperiod equal to the reciprocal of the delay, is apparent in each curve616. The amplitude of the dominant oscillation in absorption showsdiminishing strength with increasing delay due to homogeneous dephasing.

FIG. 6B is a graph 620 that illustrates peaks in cross correlationcurves generated by taking the Fourier transform of the readout signalsof FIG. 6A, according to an embodiment. The time axis 622 indicates thedelay time between the two interacting pulses. The amplitude axis 624indicates the relative signal strength of the correlation with delay.Each curve 626 a through 626 p represents the cross correlation of acorresponding readout signal in FIG. 6A. Each curve 626 is displacedvertically a different amount to allow features to be viewed. The fixedvalue of the delay increases from 0.5 μs for curve 616 a through 2.0 μsfor curve 616 p, at 0.1 μs per curve.

The Fourier transform that produces curves 626 shows frequency analysisof the corresponding curves 616, to reveal the programmed time delayscorresponding to the dominant oscillation in absorption. The amplitudesof curves 626 are the magnitude squared of the Fast Fourier Transform ofthe curves 616, plotted on a linear scale. The primary peaks representthe extracted time delay. The amplitudes of curves 626 are normalized sothat the major peak has the same height in each curve 626 to better showthe locations of the primary peaks. Analysis of the delay time at thepeaks' centers showed a delay resolution of about 1 ns, expected for anapproximately 15 MHz probe bandwidth.

The non-normalized data exhibits decaying peak strength with increasingdelay due to material dephasing. For one set of shots with 25 mW andanother set of shots with 40 mW power, the peak strength was fit to afirst order exponential decay, of the form exp(−2τ_(D)/T2) to deriveestimates of T2 for the material. T2 values of 0.84 μs and 0.79 μs,respectively, were obtained. The slight decrease in coherence time withhigher processing power is attributed to spectral diffusion.

FIG. 6C is a graph 630 that illustrates a comparison between crosscorrelation curves generated from readout signals for pulses with fixeddelay after different numbers of shots of such pulses, according to anembodiment. The time axis 632 indicates the delay time between the twointeracting pulses. The amplitude axis 634 indicates the relative signalstrength of the correlation with delay, plotted on a logarithmic scaleto show more structure at low signal strength. Both curves 636 a and 636b were derived from readout signals produced by 40 mW power interactingpulses with τ_(D)=0.5 μs. Curve 636 a is based on a readout signalproduced after 100 shots (N=100); and curve 636 b is based on a readoutsignal produced after 200 shots N=200). Post processing of the raw datathat produced these traces consisted of filtering to minimize the stronglow-frequency components of the unabsorbed chirped pulse envelope,performing a FFT on the result and plotting its magnitude squared.

The figure is broken into four regions 631: 631 a (region I) containsthe primary peak representing the time delay; 631 b (region II) containsthe fight temporal correlation sidelobes (RSL); 631 c (region III)contains the second harmonic 2τ_(D) of the primary peak; and 631 d(region I) contains the system background noise. The peak temporal widthis about 65 ns (full width at half maximum) as set by the probingbandwidth Br. The two traces show that the signal strengths increaseafter doubling N.

FIG. 6D is a graph 640 a that illustrates a dependence on the number ofshots for signal strength in different portions of a cross correlationcurve for two pulses with fixed delay, for a particular pulse power,according to an embodiment. FIG. 6E is a graph 640 b that illustrates asimilar dependence for a different pulse power, according to anembodiment. In both graphs 640 a, 640 b, the horizontal axis 642 a, 642b, respectively, represents a number of shots N during the integrationof the interaction absorption spectrum on a logarithmic scale to showmore structure at low numbers of shots. In both graphs, the verticalaxis 644 a, 644 b, respectively, is the rms signal strength in arbitraryunits on a logarithmic scale to show more structure at low signalstrength. In both graphs, the value of τ_(D)=0.5 μs. Graph 640 a is forshots with pulse power of 40 mW; and graph 640 b is for shots with alower pulse power of 25 mW.

Points 646 a and 646 b represent the calculated rms values for region I,versus number of processing shots at 40 mW and 25 mW, respectively. In646 a, region I, represented by points 646 a, increases as N^(1.65)(thus α=0.825, based on a non-linear fit showing 0.99 agreement) up to acompression point at about 140 shots, then approaches a steady state, asshown by the data point at N=800.

Points 648 a and 648 b represent the calculated rms values for regionIII versus number of processing shots at 40 mW and 25 mW, respectively.In graph 640 a, the second harmonic in region III, remains in the noisefloor until about N=50 shots, and then grows as N^(2.44) (based on anon-linear fit showing 0.98 agreement) up to 200 shots.

Graph 640 b shows the effect of a lower processing power under otherwiseidentical conditions. Here, the peak represented by points 646 bincreases as N^(1.57) (thus α=0.785, based on a non-linear fit showing0.98 agreement) for 200 shots, reaching strength roughly half of thevalues reached by points 646 a. At N=90, the second harmonic,represented by points 648 b, grows as N^(2.36) up to 200 shots (based ona non-linear fit with 0.76 agreement).

Points 647 a and 647 b represent the calculated rms values for region IIversus number of processing shots at 40 mW and 25 mW, respectively.Points 649 a and 649 b represent the calculated rms values for region IVversus number of processing shots at 40 mW and 25 mW, respectively. Thecalculated relative strengths of regions I, II and III include frequencycomponents that offset them above the noise floor, due to the AOMfrequency response function and imperfect post processing techniques,limiting absolute comparison between the regions. However, it isinteresting to note the relatively flat nature of region II, especiallyfor 25 mW processing power. This reveals the effect of dynamic codingfor each shot on the accumulation of the temporal sidelobe for region IIuntil nonlinearities dominate.

12.2 Demonstration Near 793 nm

Recent experimental results of baseband signal processing of 1 GHz BPSKsignals are presented in this section, showing: 1) time delay andresolution, 2) coherent integration of correlations, and 3) dynamicpattern processing.

An optical beam stabilized to sub-10 kHz over 10 ms by locking to atransient spectral hole in Tm:YAG, is electro-optically encoded andamplified with injection locking before irradiating the IBT material. Anexperimental setup for this demonstration has been assembled utilizingexisting technology and materials. FIG. 5B is a block diagram thatillustrates the experimental setup 590 for demonstrating delayprocessing, according to an embodiment near 793 nm

A cw Ti:Sapphire laser 512 b is centered at 793.377 nm and frequencystabilized to a transient spectral hole in one spatial location of a 4mm long Tm:YAG (0.1 at. %) material 560 b at 5.0 K using lock 515 b. Thestabilized laser was split into two beams 503 e, 503 d by beam splitter540 c for processing and readout, respectively. The processing beamalong optical path 503 e was modulated by an electro-optic phasemodulator (EOM) 522 b driven by a pulse pattern generator 526 b. Theoptical carrier beam was continuously BPSK modulated, such that eachpattern was modulated at 1 Gbps onto the modulated optical beams; andbetween any patterns the light was square wave ( . . . 101010 . . . )modulated at 1 Gbps. After modulation, the processing beams wereamplified by injection locking a high-powered slave diode laser ininjection locking amplifier 544 b. The processing beam is directed ontothe IBT material 560 b through acousto-optic modulator (AOM) 530 c andbeam splitter 540 b. The readout beam was modulated by an acousto-opticmodulator (AOM) 530 b driven by an arbitrary waveform generator (AWG)592 that generates a linear frequency chirped pulse around a 265 MHzcarrier. A beam splitter cube 540 b was used to align the beams, whichwere focused to an approximately 50 μm spot in the IBT material 560 b.The transmitted readout beam is then incident on a 125 MHzphoto-detector 572 b. The detector results are displayed and Fouriertransformed in oscilloscope and FFT device 574 b.

Each processing shot consisted of an M-bit binary-phase shift keyed(BPSK) waveform (e.g., representing a RADAR reference signal) and asingle time delayed replica (e.g., representing a RADAR return signal).A unique pulse pair j=1, 2, . . . N was introduced every τ_(R)=1/PRF.The delay τ_(D) is fixed for all shots. Each processing shot contains aunique, zero-mean BPSK waveform and its time delayed replica. For allexperiments, M is 512, i.e., the processing waveforms were 512 bits (512ns) BPSK sequences, and the PRF was 100 kHz. The processing beam powerwas 2.5 mW. The readout beam power was 100 μW and chirped over about 40MHz at a rate sufficient to resolve the longest time delay. The chirprate was less than (1/τ_(Dmax))², where τ_(Dmax) is the maximumresolvable delay, in order to ensure sufficient spectral resolution. Forexample, if the chirp rate is 1.0 MHz/μs, then for 1 GHz gratingbandwidth, the latency is 1.0 ms, and the required detection bandwidthis 1 MHz. Higher readout bandwidths give larger dynamic ranges.

FIG. 7A is a graph 710 that illustrates a dependence on the delay timeof a peak in a cross correlation derived from a readout signal from anIBT material, according to this embodiment. The horizontal axis 712 isdelay time. The vertical axis is signal strength in dB for the logmagnitude squared of the Fast Fourier Transform of a digital signalderived from the readout signal. Curves 716 a thorough 716 e(collectively referenced hereinafter as curves 716) show the results ofprocessed time delays ranging from 0.6 to 1.0 μs, respectively, inincrements of 0.1 μs.

The peak widths depend on the readout bandwidth and the peak signaldecreases with increasing time delay due to finite material coherencetime. Under these conditions, dynamic range >40 dB and range jitter <1ns are observed. Higher temporal resolution and dynamic range can beexpected at higher readout bandwidths.

FIG. 7B is a graph 720 that illustrates a dependence on power and numberof shots for the peak in a cross correlation derived from a readoutsignal, according to an embodiment. The horizontal axis 722 representsnumbers of shots N during integration, on a logarithmic scale. Thevertical axis represents rms peak signal strength in dB, which islogarithmic in amplitude. The points 726 a represent the dependence onnumber of shots for 2.5 mW processing power. The points 726 b, 726 c,726 d represent the dependence on number of shots for other processingpowers, respectively, decreasing by factors of 2. Ideal coherentaccumulation, proportional to N², is shown for the corresponding powersin lines 728 a, 728 b, 728 c, 728 d, respectively.

All points 726 a, 726, 726 c, 726 d (collectively referenced hereinafteras points 726) represent processing pulses with a fixed delay (τ_(D)=1μs). The processing powers are 2.5 mW, 1.25 mW, 0.625 mW and 0.3125 mWfor points 726 a, 726 b, 726 c, 726 d, respectively. Each set of pointsshows that the processed signal strength initially grows ideally as thesquare of the number of shots, as expected, but then exhibits powerdependent roll-off, due to saturation, before reaching a steady state.In general, for lower power, more shots can be ideally coherentlyintegrated. For 0.3125 mW, the saturation point is roughly 85 shots,while for 2.5 mW it is roughly 15 shots. When the power is raised to 5mW (not shown) the integration varied, indicating coherent saturation ofthe individual processing shots.

Dynamic or agile coding is a desirable feature for advanced RADARsystems. FIG. 7C is a graph 730 that illustrates a dependence on numberof shots for the peak in a cross correlation derived from a readoutsignal using multiple pulse patterns, according to an embodiment. Thehorizontal axis 732 represents numbers of shots N during integration, ona logarithmic scale. The vertical axis represents rms signal strength indB, which is logarithmic in amplitude. The points 736 a represent thesignal strength of the peak and the points 736 b, represent the signalstrength of the left side lobes (for delays shorter than the peak delay)for agile coding. The difference is a measure of the dynamic range ofthe processing to discover the peak and the corresponding delay. Thepoints 737 a represent the signal strength of the peak and the points737 b, represent the signal strength of the left side lobes for singlepattern coding.

FIG. 7D is a graph 740 that illustrates a dependence or multiple pulsepatterns of the cross correlation derived from a readout signal,according to an embodiment. The horizontal axis 742 is time, and thevertical axis 744 is signal strength in dB, which is logarithmic inamplitude. Curve 746 represents the cross correlation after 800 shotsusing different codes in different shots (agile coding). Curve 747represents the cross correlation after 800 shots using the same code inevery shot (single pattern coding).

FIG. 7C shows the evolution of the signal and side-lobe strengths foragile and single pattern processing. The signal growth for both isnearly identical. But, while the fixed side lobes of single pattern growwith the signal, the varying side-lobes of dynamic patterns average out.FIG. 7D shows the difference between the full cross correlation curvesfor agile and single pattern processing after 800 shots. An enhancementof about 25 dB in dynamic range was achieved under these conditionsusing dynamic coding at 800 shots compared to single pattern coding.

12.3 Further Demonstration Near 793 nm

Recent experimental results were also obtained with 2.5 GHz BPSKbaseband signals and also with a 1.0 GHz baseband mixed up onto a 1.75GHz RF carrier. Those results extended the demonstration of analogprocessing of higher bandwidth signals and to high bandwidth signals onintermediate frequencies.

13. Digital Processor Overview

FIG. 8 is a block diagram that illustrates a computer system 800 uponwhich an embodiment of the invention may be implemented. Computer system800 includes a communication mechanism such as a bus 810 for passinginformation between other internal and external components of thecomputer system 800. Information is represented as physical signals of ameasurable phenomenon, typically electric voltages, but including, inother embodiments, such phenomena as magnetic, electromagnetic,pressure, chemical, molecular and atomic interactions. For example,north and south magnetic fields, or a zero and non-zero electricvoltage, represent two states (0, 1) of a binary digit (bit). A sequenceof binary digits constitutes digital data that is used to represent anumber or code for a character. A bus 810 includes many parallelconductors of information so that information is transferred quicklyamong devices coupled to the bus 810. One or more processors 802 forprocessing information are coupled with the bus 810. A processor 802performs a set of operations on information. The set of operationsinclude bringing information in from the bus 810 and placing informationon the bus 810. The set of operations also typically include comparingtwo or more units of information, shifting positions of units ofinformation, and combining two or more units or information, such as byaddition or multiplication. A sequence of operations to be executed bythe processor 802 constitutes computer instructions.

Computer system 800 also includes a memory 804 coupled to bus 810. Thememory 804, such as a random access memory (RAM) or other dynamicstorage device, stores information including computer instructions.Dynamic memory allows information stored therein to be changed by thecomputer system 800. RAM allows a unit of information stored at alocation called a memory address to be stored and retrievedindependently of information at neighboring addresses. The memory 804 isalso used by the processor 802 to store temporary values duringexecution of computer instructions. The computer system 800 alsoincludes a read only memory (ROM) 806 or other static storage devicecoupled to the bus 810 for storing static information, includinginstructions, that is not changed by the computer system 800. Alsocoupled to bus 810 is a non-volatile (persistent) storage device 808,such as a magnetic disk or optical disk, for storing information,including instructions, that persists even when the computer system 800is turned off or otherwise loses power.

Information, including instructions, is provided to the bus 810 for useby the processor from an external input device 812, such as a keyboardcontaining alphanumeric keys operated by a human user, or a sensor. Asensor detects conditions in its vicinity and transforms thosedetections into signals compatible with the signals used to representinformation in computer system 800. Other external devices coupled tobus 810, used primarily for interacting with humans, include a displaydevice 814, such as a cathode ray tube (CRT) or a liquid crystal display(LCD), for presenting images, and a pointing device 816, such as a mouseor a trackball or cursor direction keys, for controlling a position of asmall cursor image presented on the display 814 and issuing commandsassociated with graphical elements presented on the display 814.

In the illustrated embodiment, special purpose hardware, such as anapplication specific integrated circuit (IC) 820, is coupled to bus 810.The special purpose hardware is configured to perform operations notperformed by processor 802 quickly enough for special purposes. Examplesof application specific ICs include graphics accelerator cards forgenerating images for display 814, cryptographic boards for encryptingand decrypting messages sent over a network, speech recognition, andinterfaces to special external devices, such as robotic arms and medicalscanning, equipment that repeatedly perform some complex sequence ofoperations that are more efficiently implemented in hardware.

Computer system 800 also includes one or more instances of acommunications interface 870 coupled to bus 810. Communication interface870 provides a two-way communication coupling to a variety of externaldevices that operate with their own processors, such as printers,scanners and external disks. In general the coupling is with a networklink 878 that is connected to a local network 880 to which a variety ofexternal devices with their own processors are connected. For example,communication interface 870 may be a parallel port or a serial port or auniversal serial bus (USB) port on a personal computer. In someembodiments, communications interface 870 is an integrated servicesdigital network (ISDN) card or a digital subscriber line (DSL) card or atelephone modem that provides an information communication connection toa corresponding type of telephone line. In some embodiments, acommunication interface 870 is a cable modem that converts signals onbus 810 into signals for a communication connection over a coaxial cableor into optical signals for a communication connection over a fiberoptic cable. As another example, communications interface 870 may be alocal area network (LAN) crud to provide a data communication connectionto a compatible LAN, such as Ethernet. Wireless links may also beimplemented. For wireless links, the communications interface 870 sendsand receives electrical, acoustic or electromagnetic signals, includinginfrared and optical signals that carry information streams, such asdigital data. Such signals are examples of carrier waves.

The term computer-readable medium is used herein to refer to any mediumthat participates in providing instructions to processor 802 forexecution. Such a medium may take many forms, including, but not limitedto, non-volatile media, volatile media and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device 808. Volatile media include, for example, dynamicmemory 804. Transmission media include, for example, coaxial cables,copper wire, fiber optic cables, and waves that travel through spacewithout wires or cables, such as acoustic waves and electromagneticwaves, including radio, optical and infrared waves. Signals that aretransmitted over transmission media are herein called carrier waves.

Common forms of computer-readable media include, for example, a floppydisk, a flexible disk, a hard disk, a magnetic tape, or any othermagnetic medium, a compact disk ROM (CD-ROM), or any other opticalmedium, punch cards, paper tape, or any other physical medium withpatterns of holes, a RAM, a programmable ROM (PROM), an erasable PROM(EPROM), a FLASH-EPROM, or any other memory chip or cartridge, a carrierwave, or any other medium from which a computer can read.

Network link 878 typically provides information communication throughone or more networks to other devices that use or process theinformation. For example, network link 878 may provide a connectionthrough local network 880 to a host computer 882 or to equipment 884operated by an Internet Service Provider (ISP). ISP equipment 884 inturn provides data communication services through the public, world-widepacket-switching communication network of networks now commonly referredto as the Internet 890. A computer called a server 892 connected to theInternet provides a service in response to information received over theInternet. For example, server 822 provides information representingvideo data for presentation at display 814.

The invention is related to the use of computer system 800 forimplementing the techniques described herein. According to oneembodiment of the invention, those techniques are performed by computersystem 800 in response to processor 802 executing one or more sequencesof one or more instructions contained in memory 804. Such instructions,also called software and program code, may be lead into memory 804 fromanother computer-readable medium such as storage device 808. Executionof the sequences of instructions contained in memory 804 causesprocessor 802 to perform the method steps described herein. Inalternative embodiments, hardware, such as application specificintegrated circuit 820, may be used in place of or in combination withsoftware to implement the invention. Thus, embodiments of the inventionare not limited to any specific combination of hardware and software.

The signals transmitted over network link 878 and other networks throughcommunications interface 870, which carry information to and fromcomputer system 800, are exemplary forms of carrier waves. Computersystem 800 can send and receive information, including program code,through the networks 880, 890 among others, through network link 878 andcommunications interface 870. In an example using the Internet 890, aserver 892 transmits program code for a particular application,requested by a message sent from computer 800, through Internet 890, ISPequipment 884, local network 880 and communications interface 870. Thereceived code may be executed by processor 802 as it is received, or maybe stored in storage device 808 or other non-volatile storage for laterexecution, or both. In this manner, computer system 800 many obtainapplication program code in the form of a carrier wave.

Various forms of computer readable media may be involved in carrying oneor more sequence of instructions or data or both to processor 802 forexecution. For example, instructions and data may initially be carriedon a magnetic disk of a remote computer such as host 882. The remotecomputer loads the instructions and data into its dynamic memory andsends the instructions and data over a telephone line using a modem. Amodem local to the computer system 800 receives the instructions anddata on a telephone line and uses an infra-red transmitter to convertthe instructions and data to an infra-red signal, a carrier wave servingas the network link 87S. An infrared detector serving as communicationsinterface 870 receives the instructions and data carried in the infraredsignal and places information representing the instructions and dataonto bus 810. Bus 810 carries the information to memory 804 from whichprocessor 802 receives and executes the instructions using some of thedata sent with the instructions. The instructions and data received inmemory 804 may optionally be stored on storage device 808, either beforeor after execution by the processor 802.

In the foregoing specification, the invention has been described withreference to specific embodiments thereof. It will, however, be evidentthat various modifications and changes may be made thereto withoutdeparting from the broader spirit and scope of the invention. Thespecification and drawings are, accordingly, to be regarded in anillustrative rather than a restrictive sense.

1. A method of processing large bandwidth signals over long times,resulting in high time-bandwidth-product (TBP) signal processing,comprising the steps of: causing a first plurality of signals on opticalcarriers to interact in a material with an inhomogeneously broadenedabsorption spectrum including a plurality of homogeneously broadenedabsorption lines during about a phase coherence time of thehomogeneously broadened absorption lines to record an interactionabsorption spectrum; and within about a population recovery time for apopulation of optical absorbers in the material, reading the interactionabsorption spectrum to produce a readout signal that represents atemporal map of the interaction absorption spectrum, wherein the readoutsignal includes frequency components that relate to a processing resultof processing the first plurality of signals.
 2. The method of claim 1,wherein the material has an inhomogeneously broadened absorptionspectrum with a bandwidth greater than about one GigaHertz (10⁹ Hz) andhomogeneously broadened absorption lines with bandwidths less than about100 kiloHertz (10⁵ Hz), for processing signals with a TBP greater than10⁴.
 3. The method of claim 2, wherein a TBP of a first signal in thefirst plurality of signals is greater than 10⁴.
 4. The method of claim1, said step of reading the interaction absorption spectrum in thematerial to produce a readout signal further comprising measuringabsorption of a frequency chirped optical signal directed into thematerial.
 5. The method of claim 1, said step of reading absorption ofthe frequency claim 1, wherein the readout signal is produced with abandwidth substantially less than a minimum bandwidth of the firstplurality of signals.
 6. The method of claim 1, wherein the readoutsignal is produced with a bandwidth less than about ten MegaHertz (10⁷Hz).
 7. The method of claim 1, said step of reading the interactionabsorption spectrum further comprising modulating an optical carrier toproduce a modulated optical signal that includes a component for whichfrequency sweeps in time across a frequency band within theinhomogeneously broadened absorption spectrum; directing the modulatedoptical signal on the material; and measuring the optical absorption intime.
 8. The method of claim 1, wherein: said step of causing the firstplurality of signals to interact further comprises directing the firstplurality of signals on the optical carriers along a first spatial modein the material to record the interaction absorption spectrum thatrepresents a multiplication of spectra of the first plurality ofsignals; and said readout signal includes frequency components thatrelate to the results of correlating the first plurality of signals. 9.The method of claim 8, further comprising determining a time delaybetween two signals in the first plurality of signals based on thereadout signal.
 10. The method of claim 9, wherein: a first signal ofthe first plurality of signals represents a RADAR transmitted signal; asecond signal of the first plurality of signals represents a receivedreflected signal based on the RADAR transmitted signal reflected from atarget; the method further comprises determining a range to the targetbased on the time delay between the first signal and the second signal.11. The method of claim 9, wherein: a first signal of the firstplurality of signals represents a first component received at a firstantenna element of an antenna array; a second signal of the firstplurality of signals represents a second component received at a secondantenna element of the antenna array; the method further comprisesdetermining an angle of arrival of a signal received at the antennaarray based on the time delay between the first signal and the secondsignal.
 12. The method of claim 8, further comprising, before a firsttime on the order of the population recovery time expires after thefirst plurality of signals, performing the step of directing anadditional plurality of signals on optical carriers, of one or moreadditional pluralities of signals, along the first spatial mode in thematerial at a second time after an immediately previous plurality ofsignals, to integrate in the interaction absorption spectrum anadditional spectrum that represents a multiplication of spectra of theadditional plurality of signals.
 13. The method of claim 12, wherein:said step of directing the additional plurality of signals along thefirst spatial mode includes directing the additional plurality ofsignals which have a particular time delay that is substantively similarto a time delay in the first plurality of signals; said step of readingthe interaction absorption spectrum produces a readout signal with aparticular value for certain frequency components that are related tothe particular time delay; and the particular value is enhanced relativeto other values for other frequency components that are related to timedelays that are substantively different from the particular time delay.14. The method of claim 13, wherein: a first signal of each plurality ofsignals represents a RADAR transmitted signal; and a second signal ofeach plurality of signals represents a received reflected signal basedon the RADAR transmitted signal reflected from a target.
 15. The methodof claim 14, wherein the RADAR transmitted signal in each plurality ofsignals is the same as the RADAR transmitted signal in a differentplurality of signals.
 16. The method of claim 14, wherein the RADARtransmitted signal in each plurality of signals is different from theRADAR transmitted signal a different plurality of signals.
 17. Themethod of claim 1, said step of causing the first plurality of signalson optical carriers to interact in the material, further comprising thesteps of: modulating an optical carrier, tuned to one homogeneouslybroadened absorption line in the material, to carry each signal of theplurality of signals as a modulated optical signal; and directing eachmodulated optical signal onto the material with sufficient intensity torecord in the material the spectral content of each signal.
 18. Themethod of claim 17, said step of modulating the optical carrier furthercomprising using an electro- optic modulator (EOM) to perform at leastone of analog phase modulation and phase binary encoding of the opticalcarrier based on an input electrical signal.
 19. The method of claim 17,said step of directing each modulated optical signal onto the materialwith sufficient intensity further comprising amplifying the modulatedoptical signal and directing an amplified modulated optical signal ontothe material.
 20. The method of claim 1, wherein: said step of causingthe first plurality of signals on optical carriers to interact in thematerial to record an interaction absorption spectrum further comprisingcausing the first plurality of signals on optical carriers to interactdifferently in each spatial mode of a plurality of spatial modes torecord a plurality of interaction absorption spectra corresponding tothe plurality of spatial modes; and said step of reading the interactionabsorption spectrum to produce a readout signal further comprisesreading the plurality of interaction absorption spectra to produce aplurality of readout signals corresponding to the plurality ofinteraction absorption spectra; and wherein each readout signal of theplurality of readout signals includes frequency components that relateto a processing result of processing a plurality of signals in acorresponding spatial mode of the plurality of spatial modes.
 21. Themethod of claim 20, wherein: said step of causing the first plurality ofsignals on optical carriers to interact differently in each spatial modeof the second plurality of spatial modes further comprising frequencyshifting a particular signal from the first plurality of signals by adifferent frequency shift for each spatial mode of the second pluralityof spatial modes; and the method further comprises determining a Dopplershift based on a particular frequency shift applied at a particularspatial mode associated with a particular readout signal of theplurality of readout signals.
 22. The method of claim 21, wherein: afirst signal of the first plurality of signals represents a RADARtransmitted signal; a second signal of the first plurality of signalsrepresents a received reflected signal based on the RADAR transmittedsignal reflected from a target; said step of shifting a particularsignal from the first plurality of signals comprises shifting the firstsignal by a different frequency shift for each spatial mode of thesecond plurality of spatial modes; and said step of determining theDoppler shift further comprises selecting the particular readout signalthat provides a greatest signal strength among a plurality of signalstrengths corresponding to the plurality of readout signals.
 23. Themethod of claim 22, further comprises determining a range based on atime delay based on the particular readout signal and determining avelocity based on the Doppler shift.
 24. The method of claim 1, wherein:said step of causing the first plurality of signals on optical carriersto interact in the material, further comprises the steps of directing afirst beam of the first plurality of signals on optical carriers intothe material along a first spatial mode; and directing a differentsecond beam of the first plurality of signals on optical carriers intothe material along a different second spatial mode that intersects thefirst spatial mode inside the material; and said step of reading theinteraction absorption spectrum further comprises the steps of:directing a frequency chirp signal along a third spatial mode, phasematched to the first spatial mode and the second spatial mode; andcausing an output signal and a replica of the frequency chirp tocoherently interfere with each other to produce the readout signal. 25.An apparatus for processing high time-bandwidth-product (TBP) signals,comprising: a signal input port for receiving a signal set of one ormore pluralities of input signals; a material with an inhomogeneouslybroadened absorption spectrum including a plurality of homogeneouslybroadened absorption lines; a first optical coupler to direct aplurality of modulated optical signals based on each plurality of inputsignals in the signal set onto the material in a set of one or morespatial modes within about a phase coherence time of a homogeneouslybroadened absorption line to record an interaction absorption spectrumthat represents spectral processing of the plurality of input signals; asource of a probing signal; and a detector to measure, with time, basedon the interaction absorption spectrum and the probing signal, a readoutsignal that represents a temporal map of the interaction absorptionspectrum, wherein the readout signal includes frequency components thatrelate to a processing result of processing the first plurality ofsignals.
 26. The apparatus of claim 25, further comprising ananalog-to-digital converter (ADC) to digitize the readout signal. 27.The apparatus of claim 25, said source of the probing signal furthercomprising a source of a chirped optical signal that spans over time afrequency band in the inhomogeneously broadened absorption spectrum ofthe material.
 28. The apparatus of claim 27, wherein the detectormeasures the readout signal by measuring light transmitted through thematerial from the chirped optical signal.
 29. The apparatus of claim 27,wherein the detector measures the readout signal by measuring a coherentinteraction between a replica of the chirped optical signal and an echostimulated in the material by the chirped optical signal.
 30. Theapparatus of claim 25, further comprising a post processor to determinea processing result based on the readout signal.
 31. The apparatus ofclaim 25, further comprising: a first source of an optical carrier tunedto one homogeneously broadened absorption line; and a first modulatoroptically connected to the source of the optical carrier and connectedto the signal input port to output the plurality of modulated opticalsignals based on each plurality of input signals in the signal set. 32.The apparatus of claim 25, further comprising a second optical couplerto direct the probing signal into the material.
 33. The apparatus ofclaim 31, the source of the probing signal further comprising a secondmodulator optically connected to the first source to generate thechirped optical signal based on the optical carrier.
 34. The apparatusof claim 25, wherein the material has an inhomogeneously broadenedabsorption spectrum with a bandwidth greater than one GigaHz (10⁹ Hertz)and homogeneously broadened absorption lines with bandwidths less, thanabout 100 kiloHertz (10⁵ Hz), for processing a signal in the set of oneor more pluralities of input signals with a TBP greater than 10⁴. 35.The apparatus of claim 25, wherein the detector has a bandwidth lessthan about ten MegaHertz (10⁷ Hz).
 36. The apparatus of claim 26,wherein the ADC has a bandwidth less than about ten MegaHertz (10⁷ Hz).37. The apparatus of claim 31, the first source further comprising anexternal cavity diode laser.
 38. The apparatus of claim 31, the firstsource further comprising a frequency stabilization system in which atuned frequency is stabilized to a transient spectral hole at a spatialmode in the material different from any spatial mode in the set of oneor more spatial modes.
 39. The apparatus of claim 31, the firstmodulator further comprising one or more electro-optic phase modulators.40. The apparatus of claim 31, further comprising a high bandwidthoptical amplifier disposed between the first modulator and the firstoptical coupler to amplify the plurality of modulated optical signalssufficiently to record spectral content of the plurality of modulatedoptical signals in the material.
 41. The apparatus of claim 25, thefirst optical coupler further comprising an acousto-optic deflectorassembly to direct a frequency shifted optical signal based on anoptical signal of the plurality of optical signals into a differentspatial mode of the set of one or more spatial modes.
 42. The apparatusof claim 25, further comprising a long-life, maintenance-freeclosed-cycle cryostat to condition the material.
 43. The apparatus ofclaim 25, said detector further comprising a low-bandwidth, low-noisephoto-receiver.
 44. The apparatus of claim 26, said ADC furthercomprising a low-bandwidth, high-dynamic-range analog to digitalconverter.
 45. The apparatus of claim 25, wherein the first opticalcoupler directs each different plurality of input signals from thesignal set onto the material to integrate the spectral content of aninteraction among each plurality into the interaction absorptionspectrum before the interaction absorption spectrum decays.
 46. Theapparatus of claim 41, the acoustic-optic deflector assembly furthercomprising an AOD set of one or more acousto-optic deflectors (AODs)configured so that: an optical output path from a first AOD of the AODset is directed into an input of a second AOD of the AOD set; and anacoustic signal propagates in the second AOD in a direction opposite toa direction that an acoustic signal propagates in the first AOD.
 47. Theapparatus of claim 46, wherein the first AOD is different from thesecond AOD.
 48. The apparatus of claim 46, wherein the first AOD is thesame as the second AOD.
 49. A system for processing hightime-bandwidth-product (TBP) RADAR signals, comprising: a optical analogprocessing device comprising: a signal input port for receiving a signalset of one or more pluralities of input signals; a material with aninhomogeneously broadened absorption spectrum including a plurality ofhomogeneously broadened absorption lines; a first optical coupler todirect a plurality of modulated optical signals based on each pluralityof input signals in the signal set onto the material in a set of one ormore spatial modes within about a phase coherence time of ahomogeneously broadened absorption line to record an interactionabsorption spectrum that represents spectral processing of the pluralityof input signals; a source of a probing signal; and a detector tomeasure, with time, based on the interaction absorption spectrum and theprobing signal, a readout signal that represents a temporal map of theinteraction absorption spectrum, wherein the readout signal includesfrequency components that relate to a processing result of processingthe first plurality of signals; a RADAR signal conditioner configuredfor: selecting a first set of one or more signals based on one or moreRADAR transmitted signals, and a second set of one or more signals basedone or more received signals based on the one or more RADAR transmittedsignals after reflection from a target; and sending the first set ofsignals and the second set of signals to the signal input port of theanalog optical processing device; and a processor configured todetermine range with high resolution to the target based on the readoutsignal.
 50. The system of claim 49, said processor further configured todetermine speed of the target based on a Doppler shift of the second setof signals relative to the first set of signals based on the readoutsignal.
 51. A method of processing large bandwidth signals over longtimes, resulting in high time-bandwidth-product (TBP) signal processing,comprising the steps of: causing an input signal on an optical carrierto interact in a material with an inhomogeneously broadened absorptionspectrum including a plurality of homogeneously broadened absorptionlines to record an interaction absorption spectrum; and within about apopulation recovery time for a population of optical absorbers in thematerial, reading the interaction absorption spectrum to produce areadout signal that represents a temporal map of the interactionabsorption spectrum, wherein the readout signal indicates frequencycomponents of the input signal.